{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0001","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 1, 2], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 1, 2], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044001,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"statistic":[0,1,2],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0002","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 2, 4], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 2, 4], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044002,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"statistic":[0,2,4],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0003","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,3,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 3, 6], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 3, 6], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044003,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"statistic":[0,3,6],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0004","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,4,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 4, 8], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 4, 8], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044004,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"statistic":[0,4,8],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0005","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,5,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 5, 10], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 5, 10], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044005,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"statistic":[0,5,10],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0006","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,6,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 6, 12], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 6, 12], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044006,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"statistic":[0,6,12],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0007","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,7,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 7, 14], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 7, 14], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044007,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"statistic":[0,7,14],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0008","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 8, 16], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 8, 16], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044008,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"statistic":[0,8,16],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0009","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,9,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 9, 18], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 9, 18], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044009,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"statistic":[0,9,18],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0010","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,10,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 10, 20], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 10, 20], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044010,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"statistic":[0,10,20],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0011","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,11,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 11, 22], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 11, 22], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044011,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"statistic":[0,11,22],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0012","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,12,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 12, 24], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 12, 24], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044012,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"statistic":[0,12,24],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0013","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,13,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 13, 26], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 13, 26], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044013,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"statistic":[0,13,26],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0014","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,14,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 14, 28], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 14, 28], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044014,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"statistic":[0,14,28],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0015","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,15,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 15, 30], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 15, 30], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044015,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"statistic":[0,15,30],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0016","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,16,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 16, 32], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 16, 32], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044016,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"statistic":[0,16,32],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0017","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,17,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 17, 34], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 17, 34], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044017,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"statistic":[0,17,34],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0018","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,18,36]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 18, 36], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 18, 36], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044018,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"statistic":[0,18,36],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0019","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,19,38]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 19, 38], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 19, 38], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044019,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"statistic":[0,19,38],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0020","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,20,40]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 20, 40], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 20, 40], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044020,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"statistic":[0,20,40],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0021","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,21,42]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 21, 42], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 21, 42], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044021,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"statistic":[0,21,42],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0022","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,22,44]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 22, 44], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 22, 44], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044022,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"statistic":[0,22,44],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0023","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,23,46]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 23, 46], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 23, 46], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044023,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"statistic":[0,23,46],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0024","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,24,48]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 24, 48], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 24, 48], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044024,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"statistic":[0,24,48],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0025","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-qualification；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,25,50]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, [0, 25, 50], 是, 是, single_total_statistic_independent_of_parameter)","explanation_zh":"Wave5第四層核對=(2, 3, [0, 25, 50], 是, 是, single_total_statistic_independent_of_parameter)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-qualification","seed":202611044025,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"statistic":[0,25,50],"domain":"Finite_model_total_statistic","operation":"estimator-qualification","semantic_template":"qf-mod35-estimator-qualification/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0026","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,1,2],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044026,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"statistic":[0,1,2],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0027","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,2,4],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 2, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044027,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"statistic":[0,2,4],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0028","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,3,6],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 6, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 6, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044028,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"statistic":[0,3,6],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0029","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,4,8],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044029,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"statistic":[0,4,8],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0030","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,5,10],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 5, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044030,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"statistic":[0,5,10],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0031","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,6,12],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 12, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 12, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044031,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"statistic":[0,6,12],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0032","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,7,14],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044032,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"statistic":[0,7,14],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0033","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 8, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 8, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044033,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"statistic":[0,8,16],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0034","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,9,18],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 18, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 18, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044034,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"statistic":[0,9,18],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0035","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,10,20],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044035,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"statistic":[0,10,20],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0036","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,11,22],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 11, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 11, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044036,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"statistic":[0,11,22],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0037","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,12,24],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 24, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 24, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044037,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"statistic":[0,12,24],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0038","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,13,26],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044038,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"statistic":[0,13,26],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0039","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,14,28],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 14, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 14, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044039,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"statistic":[0,14,28],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0040","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,15,30],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 30, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 30, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044040,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"statistic":[0,15,30],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0041","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,16,32],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044041,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"statistic":[0,16,32],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0042","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,17,34],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 17, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 17, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044042,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"statistic":[0,17,34],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0043","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,18,36],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 36, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 36, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044043,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"statistic":[0,18,36],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0044","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,19,38],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044044,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"statistic":[0,19,38],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0045","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,20,40],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 20, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 20, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044045,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"statistic":[0,20,40],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0046","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,21,42],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 42, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 42, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044046,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"statistic":[0,21,42],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0047","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,22,44],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044047,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"statistic":[0,22,44],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0048","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,23,46],\"outcome\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 23, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(1, 23, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044048,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"statistic":[0,23,46],"outcome":1,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome\":1,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0049","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,24,48],\"outcome\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 48, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(2, 48, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044049,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"statistic":[0,24,48],"outcome":2,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome\":2,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0050","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-observed-estimate；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,25,50],\"outcome\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 0, estimate_value_not_estimator_function)","explanation_zh":"Wave5第四層核對=(0, 0, estimate_value_not_estimator_function)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-observed-estimate","seed":202611044050,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"statistic":[0,25,50],"outcome":0,"domain":"Finite_model_total_statistic","operation":"estimator-observed-estimate","semantic_template":"qf-mod35-estimator-observed-estimate/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome\":0,\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0051","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,1,2],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 5/4, [0, 1, 2])","explanation_zh":"Wave5第四層核對=(0, 5/4, [0, 1, 2])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044051,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"statistic":[0,1,2],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0052","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,2,4],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 4/3, [0, 2, 4])","explanation_zh":"Wave5第四層核對=(1, 4/3, [0, 2, 4])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044052,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"statistic":[0,2,4],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0053","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,3,6],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 9/2, [0, 3, 6])","explanation_zh":"Wave5第四層核對=(0, 9/2, [0, 3, 6])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044053,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"statistic":[0,3,6],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0054","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,4,8],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 8/3, [0, 4, 8])","explanation_zh":"Wave5第四層核對=(1, 8/3, [0, 4, 8])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044054,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"statistic":[0,4,8],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,4,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0055","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,5,10],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 65/8, [0, 5, 10])","explanation_zh":"Wave5第四層核對=(0, 65/8, [0, 5, 10])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044055,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"statistic":[0,5,10],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,5,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0056","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,6,12],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 4, [0, 6, 12])","explanation_zh":"Wave5第四層核對=(1, 4, [0, 6, 12])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044056,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"statistic":[0,6,12],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,6,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0057","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,7,14],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 119/10, [0, 7, 14])","explanation_zh":"Wave5第四層核對=(0, 119/10, [0, 7, 14])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044057,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"statistic":[0,7,14],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,7,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0058","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 16/3, [0, 8, 16])","explanation_zh":"Wave5第四層核對=(1, 16/3, [0, 8, 16])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044058,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"statistic":[0,8,16],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,8,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0059","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,9,18],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 63/4, [0, 9, 18])","explanation_zh":"Wave5第四層核對=(0, 63/4, [0, 9, 18])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044059,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"statistic":[0,9,18],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,9,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0060","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,10,20],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 20/3, [0, 10, 20])","explanation_zh":"Wave5第四層核對=(1, 20/3, [0, 10, 20])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044060,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"statistic":[0,10,20],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,10,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0061","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,11,22],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 275/14, [0, 11, 22])","explanation_zh":"Wave5第四層核對=(0, 275/14, [0, 11, 22])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044061,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"statistic":[0,11,22],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,11,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0062","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,12,24],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 8, [0, 12, 24])","explanation_zh":"Wave5第四層核對=(1, 8, [0, 12, 24])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044062,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"statistic":[0,12,24],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,12,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0063","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,13,26],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 377/16, [0, 13, 26])","explanation_zh":"Wave5第四層核對=(0, 377/16, [0, 13, 26])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044063,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"statistic":[0,13,26],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,13,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0064","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,14,28],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 28/3, [0, 14, 28])","explanation_zh":"Wave5第四層核對=(1, 28/3, [0, 14, 28])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044064,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"statistic":[0,14,28],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,14,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0065","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,15,30],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 55/2, [0, 15, 30])","explanation_zh":"Wave5第四層核對=(0, 55/2, [0, 15, 30])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044065,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"statistic":[0,15,30],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,15,30]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0066","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,16,32],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 32/3, [0, 16, 32])","explanation_zh":"Wave5第四層核對=(1, 32/3, [0, 16, 32])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044066,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"statistic":[0,16,32],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,16,32]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0067","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,17,34],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 629/20, [0, 17, 34])","explanation_zh":"Wave5第四層核對=(0, 629/20, [0, 17, 34])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044067,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"statistic":[0,17,34],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,17,34]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0068","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,18,36],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 12, [0, 18, 36])","explanation_zh":"Wave5第四層核對=(1, 12, [0, 18, 36])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044068,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"statistic":[0,18,36],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,18,36]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0069","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,19,38],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 779/22, [0, 19, 38])","explanation_zh":"Wave5第四層核對=(0, 779/22, [0, 19, 38])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044069,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"statistic":[0,19,38],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,19,38]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0070","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,20,40],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 40/3, [0, 20, 40])","explanation_zh":"Wave5第四層核對=(1, 40/3, [0, 20, 40])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044070,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"statistic":[0,20,40],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,20,40]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0071","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,21,42],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 315/8, [0, 21, 42])","explanation_zh":"Wave5第四層核對=(0, 315/8, [0, 21, 42])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044071,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"statistic":[0,21,42],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,21,42]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0072","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,22,44],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 44/3, [0, 22, 44])","explanation_zh":"Wave5第四層核對=(1, 44/3, [0, 22, 44])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044072,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"statistic":[0,22,44],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,22,44]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0073","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,23,46],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1127/26, [0, 23, 46])","explanation_zh":"Wave5第四層核對=(0, 1127/26, [0, 23, 46])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044073,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"statistic":[0,23,46],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,23,46]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0074","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,24,48],\"parameter\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 16, [0, 24, 48])","explanation_zh":"Wave5第四層核對=(1, 16, [0, 24, 48])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044074,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"statistic":[0,24,48],"parameter":1,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":1,\"parameter_count\":2,\"statistic\":[0,24,48]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0075","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-expectation-at-parameter；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,25,50],\"parameter\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1325/28, [0, 25, 50])","explanation_zh":"Wave5第四層核對=(0, 1325/28, [0, 25, 50])；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-expectation-at-parameter","seed":202611044075,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"statistic":[0,25,50],"parameter":0,"domain":"Finite_model_total_statistic","operation":"estimator-expectation-at-parameter","semantic_template":"qf-mod35-estimator-expectation-at-parameter/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter\":0,\"parameter_count\":2,\"statistic\":[0,25,50]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0076","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 1, 2], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044076,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],"statistic":[0,1,2],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,4],[1,4],[2,4]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0077","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 4], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 2, 4], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044077,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],"statistic":[0,2,4],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,5],[1,5],[3,5]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0078","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,3,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 6], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 3, 6], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044078,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],"statistic":[0,3,6],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,6],[1,6],[4,6]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0079","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,4,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 4, 8], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 4, 8], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044079,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],"statistic":[0,4,8],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,7],[1,7],[5,7]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,4,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0080","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,5,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 5, 10], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 5, 10], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044080,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],"statistic":[0,5,10],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,8],[1,8],[6,8]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,5,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0081","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,6,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 6, 12], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 6, 12], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044081,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],"statistic":[0,6,12],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,9],[1,9],[7,9]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,6,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0082","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,7,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 7, 14], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 7, 14], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044082,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],"statistic":[0,7,14],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,10],[1,10],[8,10]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,7,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0083","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,8,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 8, 16], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 8, 16], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044083,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],"statistic":[0,8,16],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,11],[1,11],[9,11]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,8,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0084","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,9,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 9, 18], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 9, 18], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044084,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],"statistic":[0,9,18],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,12],[1,12],[10,12]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,9,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0085","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,10,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 10, 20], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 10, 20], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044085,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],"statistic":[0,10,20],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,13],[1,13],[11,13]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,10,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0086","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,11,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 11, 22], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 11, 22], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044086,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],"statistic":[0,11,22],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,14],[1,14],[12,14]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,11,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0087","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,12,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 12, 24], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 12, 24], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044087,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],"statistic":[0,12,24],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,15],[1,15],[13,15]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,12,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0088","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,13,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 13, 26], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 13, 26], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044088,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],"statistic":[0,13,26],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,16],[1,16],[14,16]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,13,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0089","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,14,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 14, 28], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 14, 28], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044089,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],"statistic":[0,14,28],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,17],[1,17],[15,17]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,14,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0090","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,15,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 15, 30], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 15, 30], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044090,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],"statistic":[0,15,30],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,18],[1,18],[16,18]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,15,30]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0091","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,16,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 16, 32], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 16, 32], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044091,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],"statistic":[0,16,32],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,19],[1,19],[17,19]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,16,32]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0092","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,17,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 17, 34], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 17, 34], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044092,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],"statistic":[0,17,34],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,20],[1,20],[18,20]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,17,34]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0093","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,18,36]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 18, 36], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 18, 36], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044093,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],"statistic":[0,18,36],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,21],[1,21],[19,21]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,18,36]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0094","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,19,38]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 19, 38], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 19, 38], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044094,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],"statistic":[0,19,38],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,22],[1,22],[20,22]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,19,38]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0095","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,20,40]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 20, 40], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 20, 40], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044095,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],"statistic":[0,20,40],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,23],[1,23],[21,23]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,20,40]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0096","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,21,42]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 21, 42], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 21, 42], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044096,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],"statistic":[0,21,42],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,24],[1,24],[22,24]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,21,42]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0097","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,22,44]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 22, 44], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 22, 44], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044097,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],"statistic":[0,22,44],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,25],[1,25],[23,25]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,22,44]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0098","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,23,46]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 23, 46], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 23, 46], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044098,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],"statistic":[0,23,46],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,26],[1,26],[24,26]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,23,46]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0099","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,24,48]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 24, 48], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 24, 48], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044099,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],"statistic":[0,24,48],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,27],[1,27],[25,27]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,24,48]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r04-statistical-estimator-0100","batch_id":"batch-20261014-advance-20261104-r04-statistical-estimator-foundations","language":"zh-Hant","source_mko_ids":["mko-statistical-estimator"],"title_zh":"統計估計量","stem_zh":"同一有限parametric model上的單一theta-independent total statistic。操作=estimator-property-nonconclusion；資料={\"parameter_count\":2,\"outcome_count\":3,\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"statistic\":[0,25,50]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 25, 50], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)","explanation_zh":"Wave5第四層核對=([0, 25, 50], 否, 否, 否, 否, no_unbiased_consistent_sufficient_identifiable_or_posterior_claim)；依完整明示資料重算；estimator是函數且observed value才是estimate；不推unbiased consistency sufficiency identifiability posterior或完整sampling law。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["統計估計量"]},"variant":{"family_id":"qf-mod35-estimator-property-nonconclusion","seed":202611044100,"parameters":{"parameter_count":2,"outcome_count":3,"laws":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],"statistic":[0,25,50],"domain":"Finite_model_total_statistic","operation":"estimator-property-nonconclusion","semantic_template":"qf-mod35-estimator-property-nonconclusion/{\"laws\":[[[1,28],[1,28],[26,28]],[[1,2],[1,3],[1,6]]],\"outcome_count\":3,\"parameter_count\":2,\"statistic\":[0,25,50]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}