{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0001","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/8], [1, 3/8], [2, 1/4]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/8], [1, 3/8], [2, 1/4]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056001,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],"statistic":[0,0,1,2],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0002","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"statistic\":[0,0,2,3],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/13], [2, 4/13], [3, 4/13]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/13], [2, 4/13], [3, 4/13]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056002,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],"statistic":[0,0,2,3],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0003","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"statistic\":[0,0,3,4],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/10], [3, 3/10], [4, 2/5]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/10], [3, 3/10], [4, 2/5]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056003,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],"statistic":[0,0,3,4],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0004","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"statistic\":[0,0,4,5],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/3], [4, 4/15], [5, 2/5]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 1/3], [4, 4/15], [5, 2/5]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056004,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],"statistic":[0,0,4,5],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0005","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"statistic\":[0,0,5,6],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/4], [5, 1/4], [6, 1/2]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 1/4], [5, 1/4], [6, 1/2]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056005,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],"statistic":[0,0,5,6],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0006","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"statistic\":[0,0,6,7],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/17], [6, 4/17], [7, 8/17]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/17], [6, 4/17], [7, 8/17]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056006,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],"statistic":[0,0,6,7],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0007","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"statistic\":[0,0,7,8],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/14], [7, 3/14], [8, 4/7]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/14], [7, 3/14], [8, 4/7]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056007,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],"statistic":[0,0,7,8],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,7,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0008","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"statistic\":[0,0,8,9],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/19], [8, 4/19], [9, 10/19]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/19], [8, 4/19], [9, 10/19]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056008,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,8,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0009","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"statistic\":[0,0,9,10],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/16], [9, 3/16], [10, 5/8]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/16], [9, 3/16], [10, 5/8]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056009,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],"statistic":[0,0,9,10],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0010","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"statistic\":[0,0,10,11],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/21], [10, 4/21], [11, 4/7]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/21], [10, 4/21], [11, 4/7]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056010,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],"statistic":[0,0,10,11],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,10,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0011","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"statistic\":[0,0,11,12],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/6], [11, 1/6], [12, 2/3]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 1/6], [11, 1/6], [12, 2/3]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056011,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],"statistic":[0,0,11,12],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,11,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0012","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"statistic\":[0,0,12,13],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/23], [12, 4/23], [13, 14/23]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/23], [12, 4/23], [13, 14/23]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056012,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],"statistic":[0,0,12,13],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,12,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0013","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"statistic\":[0,0,13,14],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/20], [13, 3/20], [14, 7/10]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/20], [13, 3/20], [14, 7/10]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056013,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],"statistic":[0,0,13,14],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0014","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"statistic\":[0,0,14,15],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/5], [14, 4/25], [15, 16/25]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 1/5], [14, 4/25], [15, 16/25]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056014,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],"statistic":[0,0,14,15],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,14,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0015","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"statistic\":[0,0,15,16],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/22], [15, 3/22], [16, 8/11]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/22], [15, 3/22], [16, 8/11]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056015,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],"statistic":[0,0,15,16],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,15,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0016","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"statistic\":[0,0,16,17],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/27], [16, 4/27], [17, 2/3]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/27], [16, 4/27], [17, 2/3]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056016,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],"statistic":[0,0,16,17],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,16,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0017","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"statistic\":[0,0,17,18],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/8], [17, 1/8], [18, 3/4]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 1/8], [17, 1/8], [18, 3/4]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056017,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],"statistic":[0,0,17,18],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0018","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"statistic\":[0,0,18,19],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/29], [18, 4/29], [19, 20/29]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/29], [18, 4/29], [19, 20/29]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056018,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],"statistic":[0,0,18,19],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,18,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0019","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"statistic\":[0,0,19,20],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/26], [19, 3/26], [20, 10/13]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/26], [19, 3/26], [20, 10/13]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056019,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],"statistic":[0,0,19,20],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,19,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0020","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"statistic\":[0,0,20,21],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/31], [20, 4/31], [21, 22/31]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/31], [20, 4/31], [21, 22/31]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056020,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],"statistic":[0,0,20,21],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,20,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0021","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"statistic\":[0,0,21,22],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/28], [21, 3/28], [22, 11/14]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/28], [21, 3/28], [22, 11/14]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056021,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],"statistic":[0,0,21,22],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,21,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0022","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"statistic\":[0,0,22,23],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 5/33], [22, 4/33], [23, 8/11]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 5/33], [22, 4/33], [23, 8/11]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056022,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],"statistic":[0,0,22,23],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,22,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0023","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"statistic\":[0,0,23,24],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/10], [23, 1/10], [24, 4/5]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 1/10], [23, 1/10], [24, 4/5]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056023,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],"statistic":[0,0,23,24],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,23,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0024","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"statistic\":[0,0,24,25],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/7], [24, 4/35], [25, 26/35]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(1, [[0, 1/7], [24, 4/35], [25, 26/35]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056024,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],"statistic":[0,0,24,25],"parameter":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0025","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-pushforward-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,0,25,26],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 3/32], [25, 3/32], [26, 13/16]], 1, 是, pushforward_sum_over_estimator_fibres)","explanation_zh":"Wave5第五層核對=(0, [[0, 3/32], [25, 3/32], [26, 13/16]], 1, 是, pushforward_sum_over_estimator_fibres)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-pushforward-at-parameter","seed":202611056025,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],"statistic":[0,0,25,26],"parameter":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-pushforward-at-parameter","semantic_template":"qf-mod36-sampling-pushforward-at-parameter/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,25,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0026","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 2], [[0, [[0, 3/8], [1, 3/8], [2, 1/4]]], [1, [[0, 5/12], [1, 1/3], [2, 1/4]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 1, 2], [[0, [[0, 3/8], [1, 3/8], [2, 1/4]]], [1, [[0, 5/12], [1, 1/3], [2, 1/4]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056026,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],"statistic":[0,0,1,2],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0027","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"statistic\":[0,0,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2, 3], [[0, [[0, 1/3], [2, 1/3], [3, 1/3]]], [1, [[0, 5/13], [2, 4/13], [3, 4/13]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 2, 3], [[0, [[0, 1/3], [2, 1/3], [3, 1/3]]], [1, [[0, 5/13], [2, 4/13], [3, 4/13]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056027,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],"statistic":[0,0,2,3],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0028","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"statistic\":[0,0,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 3, 4], [[0, [[0, 3/10], [3, 3/10], [4, 2/5]]], [1, [[0, 5/14], [3, 2/7], [4, 5/14]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 3, 4], [[0, [[0, 3/10], [3, 3/10], [4, 2/5]]], [1, [[0, 5/14], [3, 2/7], [4, 5/14]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056028,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],"statistic":[0,0,3,4],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0029","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"statistic\":[0,0,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 4, 5], [[0, [[0, 3/11], [4, 3/11], [5, 5/11]]], [1, [[0, 1/3], [4, 4/15], [5, 2/5]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 4, 5], [[0, [[0, 3/11], [4, 3/11], [5, 5/11]]], [1, [[0, 1/3], [4, 4/15], [5, 2/5]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056029,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],"statistic":[0,0,4,5],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0030","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"statistic\":[0,0,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 5, 6], [[0, [[0, 1/4], [5, 1/4], [6, 1/2]]], [1, [[0, 5/16], [5, 1/4], [6, 7/16]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 5, 6], [[0, [[0, 1/4], [5, 1/4], [6, 1/2]]], [1, [[0, 5/16], [5, 1/4], [6, 7/16]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056030,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],"statistic":[0,0,5,6],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0031","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"statistic\":[0,0,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 6, 7], [[0, [[0, 3/13], [6, 3/13], [7, 7/13]]], [1, [[0, 5/17], [6, 4/17], [7, 8/17]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 6, 7], [[0, [[0, 3/13], [6, 3/13], [7, 7/13]]], [1, [[0, 5/17], [6, 4/17], [7, 8/17]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056031,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],"statistic":[0,0,6,7],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0032","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"statistic\":[0,0,7,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 7, 8], [[0, [[0, 3/14], [7, 3/14], [8, 4/7]]], [1, [[0, 5/18], [7, 2/9], [8, 1/2]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 7, 8], [[0, [[0, 3/14], [7, 3/14], [8, 4/7]]], [1, [[0, 5/18], [7, 2/9], [8, 1/2]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056032,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],"statistic":[0,0,7,8],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,7,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0033","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"statistic\":[0,0,8,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 8, 9], [[0, [[0, 1/5], [8, 1/5], [9, 3/5]]], [1, [[0, 5/19], [8, 4/19], [9, 10/19]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 8, 9], [[0, [[0, 1/5], [8, 1/5], [9, 3/5]]], [1, [[0, 5/19], [8, 4/19], [9, 10/19]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056033,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,8,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0034","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"statistic\":[0,0,9,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 9, 10], [[0, [[0, 3/16], [9, 3/16], [10, 5/8]]], [1, [[0, 1/4], [9, 1/5], [10, 11/20]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 9, 10], [[0, [[0, 3/16], [9, 3/16], [10, 5/8]]], [1, [[0, 1/4], [9, 1/5], [10, 11/20]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056034,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],"statistic":[0,0,9,10],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0035","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"statistic\":[0,0,10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 10, 11], [[0, [[0, 3/17], [10, 3/17], [11, 11/17]]], [1, [[0, 5/21], [10, 4/21], [11, 4/7]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 10, 11], [[0, [[0, 3/17], [10, 3/17], [11, 11/17]]], [1, [[0, 5/21], [10, 4/21], [11, 4/7]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056035,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],"statistic":[0,0,10,11],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,10,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0036","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"statistic\":[0,0,11,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 11, 12], [[0, [[0, 1/6], [11, 1/6], [12, 2/3]]], [1, [[0, 5/22], [11, 2/11], [12, 13/22]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 11, 12], [[0, [[0, 1/6], [11, 1/6], [12, 2/3]]], [1, [[0, 5/22], [11, 2/11], [12, 13/22]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056036,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],"statistic":[0,0,11,12],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,11,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0037","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"statistic\":[0,0,12,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 12, 13], [[0, [[0, 3/19], [12, 3/19], [13, 13/19]]], [1, [[0, 5/23], [12, 4/23], [13, 14/23]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 12, 13], [[0, [[0, 3/19], [12, 3/19], [13, 13/19]]], [1, [[0, 5/23], [12, 4/23], [13, 14/23]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056037,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],"statistic":[0,0,12,13],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,12,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0038","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"statistic\":[0,0,13,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 13, 14], [[0, [[0, 3/20], [13, 3/20], [14, 7/10]]], [1, [[0, 5/24], [13, 1/6], [14, 5/8]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 13, 14], [[0, [[0, 3/20], [13, 3/20], [14, 7/10]]], [1, [[0, 5/24], [13, 1/6], [14, 5/8]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056038,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],"statistic":[0,0,13,14],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0039","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"statistic\":[0,0,14,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 14, 15], [[0, [[0, 1/7], [14, 1/7], [15, 5/7]]], [1, [[0, 1/5], [14, 4/25], [15, 16/25]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 14, 15], [[0, [[0, 1/7], [14, 1/7], [15, 5/7]]], [1, [[0, 1/5], [14, 4/25], [15, 16/25]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056039,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],"statistic":[0,0,14,15],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,14,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0040","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"statistic\":[0,0,15,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 15, 16], [[0, [[0, 3/22], [15, 3/22], [16, 8/11]]], [1, [[0, 5/26], [15, 2/13], [16, 17/26]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 15, 16], [[0, [[0, 3/22], [15, 3/22], [16, 8/11]]], [1, [[0, 5/26], [15, 2/13], [16, 17/26]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056040,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],"statistic":[0,0,15,16],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,15,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0041","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"statistic\":[0,0,16,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 16, 17], [[0, [[0, 3/23], [16, 3/23], [17, 17/23]]], [1, [[0, 5/27], [16, 4/27], [17, 2/3]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 16, 17], [[0, [[0, 3/23], [16, 3/23], [17, 17/23]]], [1, [[0, 5/27], [16, 4/27], [17, 2/3]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056041,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],"statistic":[0,0,16,17],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,16,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0042","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"statistic\":[0,0,17,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 17, 18], [[0, [[0, 1/8], [17, 1/8], [18, 3/4]]], [1, [[0, 5/28], [17, 1/7], [18, 19/28]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 17, 18], [[0, [[0, 1/8], [17, 1/8], [18, 3/4]]], [1, [[0, 5/28], [17, 1/7], [18, 19/28]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056042,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],"statistic":[0,0,17,18],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0043","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"statistic\":[0,0,18,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 18, 19], [[0, [[0, 3/25], [18, 3/25], [19, 19/25]]], [1, [[0, 5/29], [18, 4/29], [19, 20/29]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 18, 19], [[0, [[0, 3/25], [18, 3/25], [19, 19/25]]], [1, [[0, 5/29], [18, 4/29], [19, 20/29]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056043,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],"statistic":[0,0,18,19],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,18,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0044","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"statistic\":[0,0,19,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 19, 20], [[0, [[0, 3/26], [19, 3/26], [20, 10/13]]], [1, [[0, 1/6], [19, 2/15], [20, 7/10]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 19, 20], [[0, [[0, 3/26], [19, 3/26], [20, 10/13]]], [1, [[0, 1/6], [19, 2/15], [20, 7/10]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056044,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],"statistic":[0,0,19,20],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,19,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0045","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"statistic\":[0,0,20,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 20, 21], [[0, [[0, 1/9], [20, 1/9], [21, 7/9]]], [1, [[0, 5/31], [20, 4/31], [21, 22/31]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 20, 21], [[0, [[0, 1/9], [20, 1/9], [21, 7/9]]], [1, [[0, 5/31], [20, 4/31], [21, 22/31]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056045,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],"statistic":[0,0,20,21],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,20,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0046","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"statistic\":[0,0,21,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 21, 22], [[0, [[0, 3/28], [21, 3/28], [22, 11/14]]], [1, [[0, 5/32], [21, 1/8], [22, 23/32]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 21, 22], [[0, [[0, 3/28], [21, 3/28], [22, 11/14]]], [1, [[0, 5/32], [21, 1/8], [22, 23/32]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056046,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],"statistic":[0,0,21,22],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,21,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0047","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"statistic\":[0,0,22,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 22, 23], [[0, [[0, 3/29], [22, 3/29], [23, 23/29]]], [1, [[0, 5/33], [22, 4/33], [23, 8/11]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 22, 23], [[0, [[0, 3/29], [22, 3/29], [23, 23/29]]], [1, [[0, 5/33], [22, 4/33], [23, 8/11]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056047,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],"statistic":[0,0,22,23],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,22,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0048","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"statistic\":[0,0,23,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 23, 24], [[0, [[0, 1/10], [23, 1/10], [24, 4/5]]], [1, [[0, 5/34], [23, 2/17], [24, 25/34]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 23, 24], [[0, [[0, 1/10], [23, 1/10], [24, 4/5]]], [1, [[0, 5/34], [23, 2/17], [24, 25/34]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056048,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],"statistic":[0,0,23,24],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,23,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0049","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"statistic\":[0,0,24,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 24, 25], [[0, [[0, 3/31], [24, 3/31], [25, 25/31]]], [1, [[0, 1/7], [24, 4/35], [25, 26/35]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 24, 25], [[0, [[0, 3/31], [24, 3/31], [25, 25/31]]], [1, [[0, 1/7], [24, 4/35], [25, 26/35]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056049,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],"statistic":[0,0,24,25],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0050","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-family-readback；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,0,25,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 25, 26], [[0, [[0, 3/32], [25, 3/32], [26, 13/16]]], [1, [[0, 5/36], [25, 1/9], [26, 3/4]]]], 是, one_theta_independent_total_statistic_family_of_laws)","explanation_zh":"Wave5第五層核對=([0, 0, 25, 26], [[0, [[0, 3/32], [25, 3/32], [26, 13/16]]], [1, [[0, 5/36], [25, 1/9], [26, 3/4]]]], 是, one_theta_independent_total_statistic_family_of_laws)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-family-readback","seed":202611056050,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],"statistic":[0,0,25,26],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-family-readback","semantic_template":"qf-mod36-sampling-family-readback/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,25,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0051","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 3/8], [1, 3/8], [2, 1/4]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056051,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],"statistic":[0,0,1,2],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0052","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"statistic\":[0,0,2,3],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 5/13], [2, 4/13], [3, 4/13]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 5/13], [2, 4/13], [3, 4/13]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056052,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],"statistic":[0,0,2,3],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0053","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"statistic\":[0,0,3,4],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, 3/10], [3, 3/10], [4, 2/5]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 3, [[0, 3/10], [3, 3/10], [4, 2/5]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056053,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],"statistic":[0,0,3,4],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0054","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"statistic\":[0,0,4,5],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 5, [[0, 1/3], [4, 4/15], [5, 2/5]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 5, [[0, 1/3], [4, 4/15], [5, 2/5]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056054,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],"statistic":[0,0,4,5],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0055","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"statistic\":[0,0,5,6],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 1/4], [5, 1/4], [6, 1/2]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 1/4], [5, 1/4], [6, 1/2]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056055,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],"statistic":[0,0,5,6],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0056","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"statistic\":[0,0,6,7],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 5/17], [6, 4/17], [7, 8/17]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 5/17], [6, 4/17], [7, 8/17]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056056,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],"statistic":[0,0,6,7],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0057","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"statistic\":[0,0,7,8],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 7, [[0, 3/14], [7, 3/14], [8, 4/7]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 7, [[0, 3/14], [7, 3/14], [8, 4/7]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056057,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],"statistic":[0,0,7,8],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,7,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0058","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"statistic\":[0,0,8,9],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 9, [[0, 5/19], [8, 4/19], [9, 10/19]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 9, [[0, 5/19], [8, 4/19], [9, 10/19]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056058,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,8,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0059","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"statistic\":[0,0,9,10],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 3/16], [9, 3/16], [10, 5/8]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 3/16], [9, 3/16], [10, 5/8]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056059,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],"statistic":[0,0,9,10],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0060","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"statistic\":[0,0,10,11],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 5/21], [10, 4/21], [11, 4/7]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 5/21], [10, 4/21], [11, 4/7]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056060,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],"statistic":[0,0,10,11],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,10,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0061","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"statistic\":[0,0,11,12],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 11, [[0, 1/6], [11, 1/6], [12, 2/3]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 11, [[0, 1/6], [11, 1/6], [12, 2/3]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056061,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],"statistic":[0,0,11,12],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,11,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0062","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"statistic\":[0,0,12,13],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 13, [[0, 5/23], [12, 4/23], [13, 14/23]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 13, [[0, 5/23], [12, 4/23], [13, 14/23]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056062,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],"statistic":[0,0,12,13],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,12,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0063","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"statistic\":[0,0,13,14],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 3/20], [13, 3/20], [14, 7/10]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 3/20], [13, 3/20], [14, 7/10]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056063,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],"statistic":[0,0,13,14],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0064","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"statistic\":[0,0,14,15],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 1/5], [14, 4/25], [15, 16/25]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 1/5], [14, 4/25], [15, 16/25]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056064,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],"statistic":[0,0,14,15],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,14,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0065","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"statistic\":[0,0,15,16],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 15, [[0, 3/22], [15, 3/22], [16, 8/11]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 15, [[0, 3/22], [15, 3/22], [16, 8/11]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056065,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],"statistic":[0,0,15,16],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,15,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0066","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"statistic\":[0,0,16,17],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 17, [[0, 5/27], [16, 4/27], [17, 2/3]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 17, [[0, 5/27], [16, 4/27], [17, 2/3]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056066,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],"statistic":[0,0,16,17],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,16,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0067","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"statistic\":[0,0,17,18],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 1/8], [17, 1/8], [18, 3/4]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 1/8], [17, 1/8], [18, 3/4]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056067,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],"statistic":[0,0,17,18],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0068","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"statistic\":[0,0,18,19],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 5/29], [18, 4/29], [19, 20/29]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 5/29], [18, 4/29], [19, 20/29]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056068,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],"statistic":[0,0,18,19],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,18,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0069","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"statistic\":[0,0,19,20],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 19, [[0, 3/26], [19, 3/26], [20, 10/13]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 19, [[0, 3/26], [19, 3/26], [20, 10/13]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056069,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],"statistic":[0,0,19,20],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,19,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0070","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"statistic\":[0,0,20,21],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 21, [[0, 5/31], [20, 4/31], [21, 22/31]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 21, [[0, 5/31], [20, 4/31], [21, 22/31]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056070,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],"statistic":[0,0,20,21],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,20,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0071","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"statistic\":[0,0,21,22],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 3/28], [21, 3/28], [22, 11/14]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 3/28], [21, 3/28], [22, 11/14]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056071,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],"statistic":[0,0,21,22],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,21,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0072","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"statistic\":[0,0,22,23],\"parameter\":1,\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 0, [[0, 5/33], [22, 4/33], [23, 8/11]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(1, 0, [[0, 5/33], [22, 4/33], [23, 8/11]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056072,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],"statistic":[0,0,22,23],"parameter":1,"outcome":1,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"outcome\":1,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,22,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0073","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"statistic\":[0,0,23,24],\"parameter\":0,\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 23, [[0, 1/10], [23, 1/10], [24, 4/5]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(2, 23, [[0, 1/10], [23, 1/10], [24, 4/5]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056073,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],"statistic":[0,0,23,24],"parameter":0,"outcome":2,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"outcome\":2,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,23,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0074","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"statistic\":[0,0,24,25],\"parameter\":1,\"outcome\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 25, [[0, 1/7], [24, 4/35], [25, 26/35]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(3, 25, [[0, 1/7], [24, 4/35], [25, 26/35]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056074,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],"statistic":[0,0,24,25],"parameter":1,"outcome":3,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"outcome\":3,\"outcome_count\":4,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,0,24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0075","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-observed-estimate-boundary；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,0,25,26],\"parameter\":0,\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [[0, 3/32], [25, 3/32], [26, 13/16]], observed_estimate_is_not_sampling_distribution)","explanation_zh":"Wave5第五層核對=(0, 0, [[0, 3/32], [25, 3/32], [26, 13/16]], observed_estimate_is_not_sampling_distribution)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-observed-estimate-boundary","seed":202611056075,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],"statistic":[0,0,25,26],"parameter":0,"outcome":0,"domain":"Finite_parametric_pushforward_laws","operation":"sampling-observed-estimate-boundary","semantic_template":"qf-mod36-sampling-observed-estimate-boundary/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome\":0,\"outcome_count\":4,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,0,25,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0076","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"statistic\":[0,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 1, 2], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 1, 2], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056076,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],"statistic":[0,0,1,2],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,8],[2,8],[3,8],[2,8]],[[2,12],[3,12],[4,12],[3,12]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0077","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"statistic\":[0,0,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2, 3], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 2, 3], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056077,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],"statistic":[0,0,2,3],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,9],[2,9],[3,9],[3,9]],[[2,13],[3,13],[4,13],[4,13]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0078","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"statistic\":[0,0,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 3, 4], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 3, 4], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056078,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],"statistic":[0,0,3,4],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,10],[2,10],[3,10],[4,10]],[[2,14],[3,14],[4,14],[5,14]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0079","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"statistic\":[0,0,4,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 4, 5], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 4, 5], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056079,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],"statistic":[0,0,4,5],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,11],[2,11],[3,11],[5,11]],[[2,15],[3,15],[4,15],[6,15]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0080","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"statistic\":[0,0,5,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 5, 6], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 5, 6], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056080,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],"statistic":[0,0,5,6],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,12],[2,12],[3,12],[6,12]],[[2,16],[3,16],[4,16],[7,16]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0081","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"statistic\":[0,0,6,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 6, 7], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 6, 7], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056081,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],"statistic":[0,0,6,7],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,13],[2,13],[3,13],[7,13]],[[2,17],[3,17],[4,17],[8,17]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0082","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"statistic\":[0,0,7,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 7, 8], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 7, 8], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056082,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],"statistic":[0,0,7,8],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,14],[2,14],[3,14],[8,14]],[[2,18],[3,18],[4,18],[9,18]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,7,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0083","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"statistic\":[0,0,8,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 8, 9], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 8, 9], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056083,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,8,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0084","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"statistic\":[0,0,9,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 9, 10], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 9, 10], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056084,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],"statistic":[0,0,9,10],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,16],[2,16],[3,16],[10,16]],[[2,20],[3,20],[4,20],[11,20]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0085","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"statistic\":[0,0,10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 10, 11], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 10, 11], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056085,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],"statistic":[0,0,10,11],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,17],[2,17],[3,17],[11,17]],[[2,21],[3,21],[4,21],[12,21]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,10,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0086","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"statistic\":[0,0,11,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 11, 12], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 11, 12], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056086,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],"statistic":[0,0,11,12],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,18],[2,18],[3,18],[12,18]],[[2,22],[3,22],[4,22],[13,22]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,11,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0087","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"statistic\":[0,0,12,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 12, 13], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 12, 13], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056087,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],"statistic":[0,0,12,13],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,19],[2,19],[3,19],[13,19]],[[2,23],[3,23],[4,23],[14,23]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,12,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0088","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"statistic\":[0,0,13,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 13, 14], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 13, 14], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056088,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],"statistic":[0,0,13,14],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,20],[2,20],[3,20],[14,20]],[[2,24],[3,24],[4,24],[15,24]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0089","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"statistic\":[0,0,14,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 14, 15], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 14, 15], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056089,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],"statistic":[0,0,14,15],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,21],[2,21],[3,21],[15,21]],[[2,25],[3,25],[4,25],[16,25]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,14,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0090","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"statistic\":[0,0,15,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 15, 16], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 15, 16], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056090,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],"statistic":[0,0,15,16],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,22],[2,22],[3,22],[16,22]],[[2,26],[3,26],[4,26],[17,26]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,15,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0091","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"statistic\":[0,0,16,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 16, 17], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 16, 17], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056091,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],"statistic":[0,0,16,17],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,23],[2,23],[3,23],[17,23]],[[2,27],[3,27],[4,27],[18,27]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,16,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0092","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"statistic\":[0,0,17,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 17, 18], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 17, 18], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056092,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],"statistic":[0,0,17,18],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,24],[2,24],[3,24],[18,24]],[[2,28],[3,28],[4,28],[19,28]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0093","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"statistic\":[0,0,18,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 18, 19], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 18, 19], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056093,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],"statistic":[0,0,18,19],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,25],[2,25],[3,25],[19,25]],[[2,29],[3,29],[4,29],[20,29]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,18,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0094","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"statistic\":[0,0,19,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 19, 20], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 19, 20], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056094,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],"statistic":[0,0,19,20],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,26],[2,26],[3,26],[20,26]],[[2,30],[3,30],[4,30],[21,30]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,19,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0095","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"statistic\":[0,0,20,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 20, 21], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 20, 21], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056095,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],"statistic":[0,0,20,21],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,27],[2,27],[3,27],[21,27]],[[2,31],[3,31],[4,31],[22,31]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,20,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0096","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"statistic\":[0,0,21,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 21, 22], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 21, 22], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056096,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],"statistic":[0,0,21,22],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,28],[2,28],[3,28],[22,28]],[[2,32],[3,32],[4,32],[23,32]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,21,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0097","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"statistic\":[0,0,22,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 22, 23], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 22, 23], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056097,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],"statistic":[0,0,22,23],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,29],[2,29],[3,29],[23,29]],[[2,33],[3,33],[4,33],[24,33]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,22,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0098","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"statistic\":[0,0,23,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 23, 24], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 23, 24], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056098,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],"statistic":[0,0,23,24],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,30],[2,30],[3,30],[24,30]],[[2,34],[3,34],[4,34],[25,34]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,23,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0099","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"statistic\":[0,0,24,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 24, 25], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 24, 25], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056099,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],"statistic":[0,0,24,25],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,31],[2,31],[3,31],[25,31]],[[2,35],[3,35],[4,35],[26,35]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r06-sampling-distribution-0100","batch_id":"batch-20261014-advance-20261105-r06-sampling-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-sampling-distribution"],"title_zh":"抽樣分布","stem_zh":"共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":4,\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"statistic\":[0,0,25,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 25, 26], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)","explanation_zh":"Wave5第五層核對=([0, 0, 25, 26], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)；依完整明示資料獨立重算；逐theta以estimator fibres加總得到pushforward law並重驗非負與總質量一；抽樣分布不是observed estimate、likelihood、posterior或參數分布；不提前宣稱無偏低變異或一致。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["抽樣分布"]},"variant":{"family_id":"qf-mod36-sampling-property-nonconclusion","seed":202611056100,"parameters":{"parameter_count":2,"outcome_count":4,"laws":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],"statistic":[0,0,25,26],"domain":"Finite_parametric_pushforward_laws","operation":"sampling-property-nonconclusion","semantic_template":"qf-mod36-sampling-property-nonconclusion/{\"laws\":[[[1,32],[2,32],[3,32],[26,32]],[[2,36],[3,36],[4,36],[27,36]]],\"outcome_count\":4,\"parameter_count\":2,\"statistic\":[0,0,25,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}