{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r04-parametric-statistical-model-0001","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/4, 1/4, 1/2], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/4, 1/4, 1/2], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034001,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0002","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/5, 1/5, 3/5], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/5, 1/5, 3/5], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034002,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0003","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/6, 1/6, 2/3], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/6, 1/6, 2/3], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034003,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0004","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/7, 1/7, 5/7], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/7, 1/7, 5/7], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034004,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0005","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/8, 1/8, 3/4], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/8, 1/8, 3/4], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034005,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0006","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/9, 1/9, 7/9], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/9, 1/9, 7/9], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034006,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0007","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/10, 1/10, 4/5], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/10, 1/10, 4/5], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034007,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0008","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/11, 1/11, 9/11], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/11, 1/11, 9/11], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034008,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0009","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/12, 1/12, 5/6], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/12, 1/12, 5/6], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034009,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0010","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/13, 1/13, 11/13], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/13, 1/13, 11/13], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034010,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0011","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/14, 1/14, 6/7], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/14, 1/14, 6/7], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034011,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0012","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/15, 1/15, 13/15], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/15, 1/15, 13/15], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034012,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0013","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/16, 1/16, 7/8], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/16, 1/16, 7/8], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034013,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0014","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/17, 1/17, 15/17], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/17, 1/17, 15/17], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034014,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0015","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/18, 1/18, 8/9], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/18, 1/18, 8/9], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034015,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0016","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/19, 1/19, 17/19], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/19, 1/19, 17/19], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034016,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0017","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/20, 1/20, 9/10], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/20, 1/20, 9/10], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034017,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0018","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/21, 1/21, 19/21], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/21, 1/21, 19/21], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034018,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0019","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/22, 1/22, 10/11], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/22, 1/22, 10/11], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034019,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0020","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/23, 1/23, 21/23], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/23, 1/23, 21/23], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034020,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0021","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/24, 1/24, 11/12], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/24, 1/24, 11/12], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034021,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0022","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/25, 1/25, 23/25], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/25, 1/25, 23/25], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034022,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0023","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/26, 1/26, 12/13], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/26, 1/26, 12/13], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034023,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0024","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/27, 1/27, 25/27], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/27, 1/27, 25/27], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034024,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0025","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]]}。請依 [parameter_count,outcome_count,law_rows,qualified,common_space] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [[0, [1/28, 1/28, 13/14], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)","explanation_zh":"Wave5第三層核對=(2, 3, [[0, [1/28, 1/28, 13/14], 1, 是], [1, [1/2, 1/3, 1/6], 1, 是]], 是, common_sample_space)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-qualification","seed":202611034025,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"domain":"Complete_finite_parametric_law_table","operation":"statmodel-qualification","semantic_template":"qf-mod34-statmodel-qualification/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0026","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/4, 是)","explanation_zh":"Wave5第三層核對=(0, 0, 1/4, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034026,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0027","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1/3, 是)","explanation_zh":"Wave5第三層核對=(1, 1, 1/3, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034027,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0028","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, 2/3, 是)","explanation_zh":"Wave5第三層核對=(0, 2, 2/3, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034028,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0029","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1/2, 是)","explanation_zh":"Wave5第三層核對=(1, 0, 1/2, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034029,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0030","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 1/8, 是)","explanation_zh":"Wave5第三層核對=(0, 1, 1/8, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034030,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0031","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/6, 是)","explanation_zh":"Wave5第三層核對=(1, 2, 1/6, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034031,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0032","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/10, 是)","explanation_zh":"Wave5第三層核對=(0, 0, 1/10, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034032,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0033","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1/3, 是)","explanation_zh":"Wave5第三層核對=(1, 1, 1/3, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034033,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0034","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, 5/6, 是)","explanation_zh":"Wave5第三層核對=(0, 2, 5/6, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034034,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0035","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1/2, 是)","explanation_zh":"Wave5第三層核對=(1, 0, 1/2, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034035,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0036","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 1/14, 是)","explanation_zh":"Wave5第三層核對=(0, 1, 1/14, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034036,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0037","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/6, 是)","explanation_zh":"Wave5第三層核對=(1, 2, 1/6, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034037,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0038","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/16, 是)","explanation_zh":"Wave5第三層核對=(0, 0, 1/16, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034038,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0039","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1/3, 是)","explanation_zh":"Wave5第三層核對=(1, 1, 1/3, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034039,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0040","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, 8/9, 是)","explanation_zh":"Wave5第三層核對=(0, 2, 8/9, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034040,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0041","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1/2, 是)","explanation_zh":"Wave5第三層核對=(1, 0, 1/2, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034041,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0042","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 1/20, 是)","explanation_zh":"Wave5第三層核對=(0, 1, 1/20, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034042,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0043","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/6, 是)","explanation_zh":"Wave5第三層核對=(1, 2, 1/6, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034043,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0044","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/22, 是)","explanation_zh":"Wave5第三層核對=(0, 0, 1/22, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034044,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0045","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1/3, 是)","explanation_zh":"Wave5第三層核對=(1, 1, 1/3, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034045,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0046","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, 11/12, 是)","explanation_zh":"Wave5第三層核對=(0, 2, 11/12, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034046,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0047","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, 1/2, 是)","explanation_zh":"Wave5第三層核對=(1, 0, 1/2, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034047,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0048","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, 1/26, 是)","explanation_zh":"Wave5第三層核對=(0, 1, 1/26, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034048,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0049","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/6, 是)","explanation_zh":"Wave5第三層核對=(1, 2, 1/6, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034049,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0050","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-law-lookup；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,probability,model_qualified] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/28, 是)","explanation_zh":"Wave5第三層核對=(0, 0, 1/28, 是)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-law-lookup","seed":202611034050,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-law-lookup","semantic_template":"qf-mod34-statmodel-law-lookup/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0051","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/4], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/4], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034051,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0052","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/5], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/5], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034052,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0053","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 2/3], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 2/3], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034053,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0054","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/7], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/7], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034054,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0055","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/8], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/8], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034055,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0056","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 7/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 7/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034056,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0057","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/10], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/10], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034057,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0058","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/11], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/11], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034058,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0059","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 5/6], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 5/6], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034059,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0060","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/13], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/13], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034060,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0061","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/14], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/14], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034061,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0062","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 13/15], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 13/15], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034062,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0063","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/16], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/16], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034063,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0064","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/17], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/17], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034064,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0065","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 8/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 8/9], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034065,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0066","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/19], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/19], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034066,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0067","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/20], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/20], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034067,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0068","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 19/21], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 19/21], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034068,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0069","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/22], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/22], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034069,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0070","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/23], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/23], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034070,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0071","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 11/12], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 11/12], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034071,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0072","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/25], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/25], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034072,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0073","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [[0, 1/26], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(1, [[0, 1/26], [1, 1/3]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034073,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0074","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 25/27], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(2, [[0, 25/27], [1, 1/6]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034074,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0075","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-likelihood；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0}。請依 [outcome,likelihood_rows,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [[0, 1/28], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)","explanation_zh":"Wave5第三層核對=(0, [[0, 1/28], [1, 1/2]], likelihood_as_function_of_parameter_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-likelihood","seed":202611034075,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-likelihood","semantic_template":"qf-mod34-statmodel-likelihood/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0076","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, parameter_index, observed_outcome, 1/4, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 0, parameter_index, observed_outcome, 1/4, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034076,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0077","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034077,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0078","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, parameter_index, observed_outcome, 2/3, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 2, parameter_index, observed_outcome, 2/3, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034078,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0079","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034079,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0080","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, parameter_index, observed_outcome, 1/8, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 1, parameter_index, observed_outcome, 1/8, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034080,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0081","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034081,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0082","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, parameter_index, observed_outcome, 1/10, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 0, parameter_index, observed_outcome, 1/10, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034082,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0083","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034083,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0084","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, parameter_index, observed_outcome, 5/6, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 2, parameter_index, observed_outcome, 5/6, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034084,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0085","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034085,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0086","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, parameter_index, observed_outcome, 1/14, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 1, parameter_index, observed_outcome, 1/14, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034086,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0087","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034087,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0088","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, parameter_index, observed_outcome, 1/16, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 0, parameter_index, observed_outcome, 1/16, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034088,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0089","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034089,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0090","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, parameter_index, observed_outcome, 8/9, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 2, parameter_index, observed_outcome, 8/9, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034090,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0091","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034091,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0092","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, parameter_index, observed_outcome, 1/20, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 1, parameter_index, observed_outcome, 1/20, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034092,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0093","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034093,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0094","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, parameter_index, observed_outcome, 1/22, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 0, parameter_index, observed_outcome, 1/22, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034094,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0095","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 1, parameter_index, observed_outcome, 1/3, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034095,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0096","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 2, parameter_index, observed_outcome, 11/12, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 2, parameter_index, observed_outcome, 11/12, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034096,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0097","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 0, parameter_index, observed_outcome, 1/2, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034097,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0098","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":1}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1, parameter_index, observed_outcome, 1/26, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 1, parameter_index, observed_outcome, 1/26, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034098,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":1,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0099","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"parameter\":1,\"outcome\":2}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(1, 2, parameter_index, observed_outcome, 1/6, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034099,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"parameter":1,"outcome":2,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式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-20261103-r04-parametric-statistical-model-0100","batch_id":"batch-20261014-advance-20261103-r04-parametric-statistical-model-foundations","language":"zh-Hant","source_mko_ids":["mko-parametric-statistical-model"],"title_zh":"參數統計模型","stem_zh":"共同有限sample space與每個parameter的完整law row。操作=statmodel-parameter-observation-boundary；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"parameter\":0,\"outcome\":0}。請依 [parameter,outcome,parameter_role,observation_role,law_value,same_role,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, parameter_index, observed_outcome, 1/28, 否, parameter_not_observation_and_likelihood_not_posterior)","explanation_zh":"Wave5第三層核對=(0, 0, parameter_index, observed_outcome, 1/28, 否, parameter_not_observation_and_likelihood_not_posterior)；依完整明示資料重算；每列非負且精確總和1，parameter與observation分離；likelihood是parameter函數而非posterior；不暗示prior或identifiability。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["參數統計模型"]},"variant":{"family_id":"qf-mod34-statmodel-parameter-observation-boundary","seed":202611034100,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"parameter":0,"outcome":0,"domain":"Complete_finite_parametric_law_table","operation":"statmodel-parameter-observation-boundary","semantic_template":"qf-mod34-statmodel-parameter-observation-boundary/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}