{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r04-markov-inequality-0001","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/6, 1/3, 1/2], [0, 1, 3], 是, 11/6, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/6, 1/3, 1/2], [0, 1, 3], 是, 11/6, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074001,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,3],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0002","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/7, 2/7, 4/7], [0, 2, 4], 是, 20/7, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/7, 2/7, 4/7], [0, 2, 4], 是, 20/7, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074002,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,4],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,7],[2,7],[4,7]],\"values\":[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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0003","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/8, 1/4, 5/8], [0, 3, 5], 是, 31/8, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/8, 1/4, 5/8], [0, 3, 5], 是, 31/8, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074003,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,5],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0004","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/9, 2/9, 2/3], [0, 4, 6], 是, 44/9, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/9, 2/9, 2/3], [0, 4, 6], 是, 44/9, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074004,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,6],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0005","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/10, 1/5, 7/10], [0, 5, 7], 是, 59/10, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/10, 1/5, 7/10], [0, 5, 7], 是, 59/10, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074005,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,7],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0006","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/11, 2/11, 8/11], [0, 6, 8], 是, 76/11, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/11, 2/11, 8/11], [0, 6, 8], 是, 76/11, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074006,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,8],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0007","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/12, 1/6, 3/4], [0, 7, 9], 是, 95/12, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/12, 1/6, 3/4], [0, 7, 9], 是, 95/12, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074007,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,9],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0008","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/13, 2/13, 10/13], [0, 8, 10], 是, 116/13, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/13, 2/13, 10/13], [0, 8, 10], 是, 116/13, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074008,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,10],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0009","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/14, 1/7, 11/14], [0, 9, 11], 是, 139/14, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/14, 1/7, 11/14], [0, 9, 11], 是, 139/14, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074009,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,11],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0010","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/15, 2/15, 4/5], [0, 10, 12], 是, 164/15, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/15, 2/15, 4/5], [0, 10, 12], 是, 164/15, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074010,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,12],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0011","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/16, 1/8, 13/16], [0, 11, 13], 是, 191/16, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/16, 1/8, 13/16], [0, 11, 13], 是, 191/16, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074011,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,13],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0012","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/17, 2/17, 14/17], [0, 12, 14], 是, 220/17, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/17, 2/17, 14/17], [0, 12, 14], 是, 220/17, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074012,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,14],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0013","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/18, 1/9, 5/6], [0, 13, 15], 是, 251/18, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/18, 1/9, 5/6], [0, 13, 15], 是, 251/18, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074013,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,15],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0014","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/19, 2/19, 16/19], [0, 14, 16], 是, 284/19, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/19, 2/19, 16/19], [0, 14, 16], 是, 284/19, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074014,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,16],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0015","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/20, 1/10, 17/20], [0, 15, 17], 是, 319/20, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/20, 1/10, 17/20], [0, 15, 17], 是, 319/20, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074015,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,17],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0016","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/21, 2/21, 6/7], [0, 16, 18], 是, 356/21, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/21, 2/21, 6/7], [0, 16, 18], 是, 356/21, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074016,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,18],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0017","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/22, 1/11, 19/22], [0, 17, 19], 是, 395/22, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/22, 1/11, 19/22], [0, 17, 19], 是, 395/22, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074017,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,19],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0018","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/23, 2/23, 20/23], [0, 18, 20], 是, 436/23, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/23, 2/23, 20/23], [0, 18, 20], 是, 436/23, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074018,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,20],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0019","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/24, 1/12, 7/8], [0, 19, 21], 是, 479/24, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/24, 1/12, 7/8], [0, 19, 21], 是, 479/24, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074019,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,21],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0020","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/25, 2/25, 22/25], [0, 20, 22], 是, 524/25, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/25, 2/25, 22/25], [0, 20, 22], 是, 524/25, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074020,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,22],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0021","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/26, 1/13, 23/26], [0, 21, 23], 是, 571/26, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/26, 1/13, 23/26], [0, 21, 23], 是, 571/26, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074021,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,23],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0022","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/27, 2/27, 8/9], [0, 22, 24], 是, 620/27, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/27, 2/27, 8/9], [0, 22, 24], 是, 620/27, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074022,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,24],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0023","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/28, 1/14, 25/28], [0, 23, 25], 是, 671/28, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/28, 1/14, 25/28], [0, 23, 25], 是, 671/28, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074023,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,25],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0024","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/29, 2/29, 26/29], [0, 24, 26], 是, 724/29, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/29, 2/29, 26/29], [0, 24, 26], 是, 724/29, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074024,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,26],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0025","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-qualification；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/30, 1/15, 9/10], [0, 25, 27], 是, 779/30, 是, finite_expectation_and_nonnegative_almost_sure)","explanation_zh":"Wave6根層核對=([1/30, 1/15, 9/10], [0, 25, 27], 是, 779/30, 是, finite_expectation_and_nonnegative_almost_sure)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-qualification","seed":202611074025,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,27],"domain":"Finite_rational_Markov_inequality","operation":"markov-qualification","semantic_template":"qf-mod38-markov-qualification/{\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0026","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,3],\"threshold\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/2, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(2, 1/2, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074026,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,3],"threshold":2,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,6],[2,6],[3,6]],\"threshold\":2,\"values\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0027","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,4],\"threshold\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 4/7, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(3, 4/7, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074027,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,4],"threshold":3,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,7],[2,7],[4,7]],\"threshold\":3,\"values\":[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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0028","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,5],\"threshold\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5/8, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(4, 5/8, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074028,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,5],"threshold":4,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,8],[2,8],[5,8]],\"threshold\":4,\"values\":[0,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0029","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,6],\"threshold\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 2/3, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(5, 2/3, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074029,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,6],"threshold":5,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,9],[2,9],[6,9]],\"threshold\":5,\"values\":[0,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0030","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,7],\"threshold\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 7/10, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(6, 7/10, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074030,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,7],"threshold":6,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,10],[2,10],[7,10]],\"threshold\":6,\"values\":[0,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0031","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,8],\"threshold\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 8/11, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(7, 8/11, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074031,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,8],"threshold":7,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,11],[2,11],[8,11]],\"threshold\":7,\"values\":[0,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0032","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,9],\"threshold\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 3/4, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(8, 3/4, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074032,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,9],"threshold":8,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,12],[2,12],[9,12]],\"threshold\":8,\"values\":[0,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0033","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,10],\"threshold\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 10/13, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(9, 10/13, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074033,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,10],"threshold":9,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,13],[2,13],[10,13]],\"threshold\":9,\"values\":[0,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0034","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,11],\"threshold\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 11/14, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(10, 11/14, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074034,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,11],"threshold":10,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,14],[2,14],[11,14]],\"threshold\":10,\"values\":[0,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0035","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,12],\"threshold\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 4/5, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(11, 4/5, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074035,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,12],"threshold":11,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,15],[2,15],[12,15]],\"threshold\":11,\"values\":[0,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0036","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,13],\"threshold\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 13/16, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(12, 13/16, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074036,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,13],"threshold":12,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,16],[2,16],[13,16]],\"threshold\":12,\"values\":[0,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0037","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,14],\"threshold\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 14/17, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(13, 14/17, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074037,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,14],"threshold":13,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,17],[2,17],[14,17]],\"threshold\":13,\"values\":[0,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0038","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,15],\"threshold\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 5/6, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(14, 5/6, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074038,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,15],"threshold":14,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,18],[2,18],[15,18]],\"threshold\":14,\"values\":[0,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0039","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,16],\"threshold\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 16/19, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(15, 16/19, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074039,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,16],"threshold":15,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,19],[2,19],[16,19]],\"threshold\":15,\"values\":[0,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0040","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,17],\"threshold\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 17/20, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(16, 17/20, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074040,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,17],"threshold":16,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,20],[2,20],[17,20]],\"threshold\":16,\"values\":[0,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0041","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,18],\"threshold\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 6/7, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(17, 6/7, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074041,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,18],"threshold":17,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,21],[2,21],[18,21]],\"threshold\":17,\"values\":[0,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0042","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,19],\"threshold\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 19/22, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(18, 19/22, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074042,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,19],"threshold":18,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,22],[2,22],[19,22]],\"threshold\":18,\"values\":[0,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0043","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,20],\"threshold\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 20/23, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(19, 20/23, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074043,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,20],"threshold":19,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,23],[2,23],[20,23]],\"threshold\":19,\"values\":[0,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0044","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,21],\"threshold\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 7/8, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(20, 7/8, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074044,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,21],"threshold":20,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,24],[2,24],[21,24]],\"threshold\":20,\"values\":[0,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0045","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,22],\"threshold\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 22/25, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(21, 22/25, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074045,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,22],"threshold":21,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,25],[2,25],[22,25]],\"threshold\":21,\"values\":[0,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0046","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,23],\"threshold\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 23/26, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(22, 23/26, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074046,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,23],"threshold":22,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,26],[2,26],[23,26]],\"threshold\":22,\"values\":[0,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0047","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,24],\"threshold\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 8/9, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(23, 8/9, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074047,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,24],"threshold":23,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,27],[2,27],[24,27]],\"threshold\":23,\"values\":[0,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0048","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,25],\"threshold\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 25/28, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(24, 25/28, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074048,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,25],"threshold":24,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,28],[2,28],[25,28]],\"threshold\":24,\"values\":[0,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0049","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,26],\"threshold\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 26/29, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(25, 26/29, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074049,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,26],"threshold":25,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,29],[2,29],[26,29]],\"threshold\":25,\"values\":[0,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0050","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-tail-probability；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,27],\"threshold\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(26, 9/10, exact_complete_finite_tail)","explanation_zh":"Wave6根層核對=(26, 9/10, exact_complete_finite_tail)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-tail-probability","seed":202611074050,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,27],"threshold":26,"domain":"Finite_rational_Markov_inequality","operation":"markov-tail-probability","semantic_template":"qf-mod38-markov-tail-probability/{\"masses\":[[1,30],[2,30],[27,30]],\"threshold\":26,\"values\":[0,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0051","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,3],\"threshold\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 11/6, 11/12, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(1/2, 11/6, 11/12, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074051,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,3],"threshold":2,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,6],[2,6],[3,6]],\"threshold\":2,\"values\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0052","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,4],\"threshold\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/7, 20/7, 20/21, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(4/7, 20/7, 20/21, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074052,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,4],"threshold":3,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,7],[2,7],[4,7]],\"threshold\":3,\"values\":[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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0053","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,5],\"threshold\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/8, 31/8, 31/32, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(5/8, 31/8, 31/32, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074053,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,5],"threshold":4,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,8],[2,8],[5,8]],\"threshold\":4,\"values\":[0,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0054","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,6],\"threshold\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, 44/9, 44/45, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(2/3, 44/9, 44/45, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074054,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,6],"threshold":5,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,9],[2,9],[6,9]],\"threshold\":5,\"values\":[0,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0055","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,7],\"threshold\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/10, 59/10, 59/60, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(7/10, 59/10, 59/60, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074055,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,7],"threshold":6,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,10],[2,10],[7,10]],\"threshold\":6,\"values\":[0,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0056","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,8],\"threshold\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/11, 76/11, 76/77, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(8/11, 76/11, 76/77, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074056,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,8],"threshold":7,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,11],[2,11],[8,11]],\"threshold\":7,\"values\":[0,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0057","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,9],\"threshold\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 95/12, 95/96, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(3/4, 95/12, 95/96, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074057,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,9],"threshold":8,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,12],[2,12],[9,12]],\"threshold\":8,\"values\":[0,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0058","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,10],\"threshold\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/13, 116/13, 116/117, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(10/13, 116/13, 116/117, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074058,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,10],"threshold":9,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,13],[2,13],[10,13]],\"threshold\":9,\"values\":[0,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0059","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,11],\"threshold\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/14, 139/14, 139/140, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(11/14, 139/14, 139/140, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074059,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,11],"threshold":10,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,14],[2,14],[11,14]],\"threshold\":10,\"values\":[0,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0060","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,12],\"threshold\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, 164/15, 164/165, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(4/5, 164/15, 164/165, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074060,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,12],"threshold":11,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,15],[2,15],[12,15]],\"threshold\":11,\"values\":[0,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0061","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,13],\"threshold\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/16, 191/16, 191/192, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(13/16, 191/16, 191/192, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074061,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,13],"threshold":12,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,16],[2,16],[13,16]],\"threshold\":12,\"values\":[0,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0062","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,14],\"threshold\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/17, 220/17, 220/221, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(14/17, 220/17, 220/221, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074062,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,14],"threshold":13,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,17],[2,17],[14,17]],\"threshold\":13,\"values\":[0,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0063","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,15],\"threshold\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, 251/18, 251/252, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(5/6, 251/18, 251/252, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074063,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,15],"threshold":14,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,18],[2,18],[15,18]],\"threshold\":14,\"values\":[0,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0064","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,16],\"threshold\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/19, 284/19, 284/285, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(16/19, 284/19, 284/285, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074064,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,16],"threshold":15,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,19],[2,19],[16,19]],\"threshold\":15,\"values\":[0,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0065","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,17],\"threshold\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/20, 319/20, 319/320, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(17/20, 319/20, 319/320, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074065,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,17],"threshold":16,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,20],[2,20],[17,20]],\"threshold\":16,\"values\":[0,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0066","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,18],\"threshold\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, 356/21, 356/357, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(6/7, 356/21, 356/357, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074066,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,18],"threshold":17,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,21],[2,21],[18,21]],\"threshold\":17,\"values\":[0,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0067","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,19],\"threshold\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/22, 395/22, 395/396, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(19/22, 395/22, 395/396, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074067,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,19],"threshold":18,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,22],[2,22],[19,22]],\"threshold\":18,\"values\":[0,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0068","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,20],\"threshold\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/23, 436/23, 436/437, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(20/23, 436/23, 436/437, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074068,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,20],"threshold":19,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,23],[2,23],[20,23]],\"threshold\":19,\"values\":[0,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0069","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,21],\"threshold\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, 479/24, 479/480, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(7/8, 479/24, 479/480, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074069,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,21],"threshold":20,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,24],[2,24],[21,24]],\"threshold\":20,\"values\":[0,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0070","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,22],\"threshold\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/25, 524/25, 524/525, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(22/25, 524/25, 524/525, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074070,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,22],"threshold":21,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,25],[2,25],[22,25]],\"threshold\":21,\"values\":[0,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0071","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,23],\"threshold\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/26, 571/26, 571/572, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(23/26, 571/26, 571/572, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074071,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,23],"threshold":22,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,26],[2,26],[23,26]],\"threshold\":22,\"values\":[0,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0072","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,24],\"threshold\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, 620/27, 620/621, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(8/9, 620/27, 620/621, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074072,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,24],"threshold":23,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,27],[2,27],[24,27]],\"threshold\":23,\"values\":[0,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0073","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,25],\"threshold\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25/28, 671/28, 671/672, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(25/28, 671/28, 671/672, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074073,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,25],"threshold":24,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,28],[2,28],[25,28]],\"threshold\":24,\"values\":[0,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0074","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,26],\"threshold\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(26/29, 724/29, 724/725, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(26/29, 724/29, 724/725, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074074,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,26],"threshold":25,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,29],[2,29],[26,29]],\"threshold\":25,\"values\":[0,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0075","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-bound-comparison；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,27],\"threshold\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, 779/30, 779/780, 是, upper_bound_not_tail_equality)","explanation_zh":"Wave6根層核對=(9/10, 779/30, 779/780, 是, upper_bound_not_tail_equality)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-bound-comparison","seed":202611074075,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,27],"threshold":26,"domain":"Finite_rational_Markov_inequality","operation":"markov-bound-comparison","semantic_template":"qf-mod38-markov-bound-comparison/{\"masses\":[[1,30],[2,30],[27,30]],\"threshold\":26,\"values\":[0,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0076","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-1,3],\"threshold\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-1, 3], 否, 1/2, 1/2, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-1, 3], 否, 1/2, 1/2, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074076,"parameters":{"masses":[[1,2],[1,2]],"values":[-1,3],"threshold":2,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":2,\"values\":[-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0077","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-2,4],\"threshold\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-2, 4], 否, 1/2, 1/3, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-2, 4], 否, 1/2, 1/3, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074077,"parameters":{"masses":[[1,2],[1,2]],"values":[-2,4],"threshold":3,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":3,\"values\":[-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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0078","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-3,5],\"threshold\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-3, 5], 否, 1/2, 1/4, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-3, 5], 否, 1/2, 1/4, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074078,"parameters":{"masses":[[1,2],[1,2]],"values":[-3,5],"threshold":4,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":4,\"values\":[-3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0079","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-4,6],\"threshold\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-4, 6], 否, 1/2, 1/5, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-4, 6], 否, 1/2, 1/5, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074079,"parameters":{"masses":[[1,2],[1,2]],"values":[-4,6],"threshold":5,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":5,\"values\":[-4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0080","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-5,7],\"threshold\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-5, 7], 否, 1/2, 1/6, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-5, 7], 否, 1/2, 1/6, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074080,"parameters":{"masses":[[1,2],[1,2]],"values":[-5,7],"threshold":6,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":6,\"values\":[-5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0081","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-6,8],\"threshold\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-6, 8], 否, 1/2, 1/7, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-6, 8], 否, 1/2, 1/7, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074081,"parameters":{"masses":[[1,2],[1,2]],"values":[-6,8],"threshold":7,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":7,\"values\":[-6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0082","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-7,9],\"threshold\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-7, 9], 否, 1/2, 1/8, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-7, 9], 否, 1/2, 1/8, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074082,"parameters":{"masses":[[1,2],[1,2]],"values":[-7,9],"threshold":8,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":8,\"values\":[-7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0083","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-8,10],\"threshold\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-8, 10], 否, 1/2, 1/9, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-8, 10], 否, 1/2, 1/9, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074083,"parameters":{"masses":[[1,2],[1,2]],"values":[-8,10],"threshold":9,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":9,\"values\":[-8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0084","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-9,11],\"threshold\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-9, 11], 否, 1/2, 1/10, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-9, 11], 否, 1/2, 1/10, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074084,"parameters":{"masses":[[1,2],[1,2]],"values":[-9,11],"threshold":10,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":10,\"values\":[-9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0085","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-10,12],\"threshold\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-10, 12], 否, 1/2, 1/11, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-10, 12], 否, 1/2, 1/11, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074085,"parameters":{"masses":[[1,2],[1,2]],"values":[-10,12],"threshold":11,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":11,\"values\":[-10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0086","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-11,13],\"threshold\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-11, 13], 否, 1/2, 1/12, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-11, 13], 否, 1/2, 1/12, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074086,"parameters":{"masses":[[1,2],[1,2]],"values":[-11,13],"threshold":12,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":12,\"values\":[-11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0087","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-12,14],\"threshold\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-12, 14], 否, 1/2, 1/13, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-12, 14], 否, 1/2, 1/13, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074087,"parameters":{"masses":[[1,2],[1,2]],"values":[-12,14],"threshold":13,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":13,\"values\":[-12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0088","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-13,15],\"threshold\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-13, 15], 否, 1/2, 1/14, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-13, 15], 否, 1/2, 1/14, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074088,"parameters":{"masses":[[1,2],[1,2]],"values":[-13,15],"threshold":14,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":14,\"values\":[-13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0089","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-14,16],\"threshold\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-14, 16], 否, 1/2, 1/15, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-14, 16], 否, 1/2, 1/15, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074089,"parameters":{"masses":[[1,2],[1,2]],"values":[-14,16],"threshold":15,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":15,\"values\":[-14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0090","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-15,17],\"threshold\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-15, 17], 否, 1/2, 1/16, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-15, 17], 否, 1/2, 1/16, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074090,"parameters":{"masses":[[1,2],[1,2]],"values":[-15,17],"threshold":16,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":16,\"values\":[-15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0091","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-16,18],\"threshold\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-16, 18], 否, 1/2, 1/17, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-16, 18], 否, 1/2, 1/17, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074091,"parameters":{"masses":[[1,2],[1,2]],"values":[-16,18],"threshold":17,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":17,\"values\":[-16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0092","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-17,19],\"threshold\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-17, 19], 否, 1/2, 1/18, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-17, 19], 否, 1/2, 1/18, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074092,"parameters":{"masses":[[1,2],[1,2]],"values":[-17,19],"threshold":18,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":18,\"values\":[-17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0093","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-18,20],\"threshold\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-18, 20], 否, 1/2, 1/19, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-18, 20], 否, 1/2, 1/19, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074093,"parameters":{"masses":[[1,2],[1,2]],"values":[-18,20],"threshold":19,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":19,\"values\":[-18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0094","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-19,21],\"threshold\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-19, 21], 否, 1/2, 1/20, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-19, 21], 否, 1/2, 1/20, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074094,"parameters":{"masses":[[1,2],[1,2]],"values":[-19,21],"threshold":20,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":20,\"values\":[-19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0095","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-20,22],\"threshold\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-20, 22], 否, 1/2, 1/21, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-20, 22], 否, 1/2, 1/21, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074095,"parameters":{"masses":[[1,2],[1,2]],"values":[-20,22],"threshold":21,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":21,\"values\":[-20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0096","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-21,23],\"threshold\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-21, 23], 否, 1/2, 1/22, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-21, 23], 否, 1/2, 1/22, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074096,"parameters":{"masses":[[1,2],[1,2]],"values":[-21,23],"threshold":22,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":22,\"values\":[-21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0097","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-22,24],\"threshold\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-22, 24], 否, 1/2, 1/23, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-22, 24], 否, 1/2, 1/23, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074097,"parameters":{"masses":[[1,2],[1,2]],"values":[-22,24],"threshold":23,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":23,\"values\":[-22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0098","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-23,25],\"threshold\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-23, 25], 否, 1/2, 1/24, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-23, 25], 否, 1/2, 1/24, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074098,"parameters":{"masses":[[1,2],[1,2]],"values":[-23,25],"threshold":24,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":24,\"values\":[-23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0099","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-24,26],\"threshold\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-24, 26], 否, 1/2, 1/25, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-24, 26], 否, 1/2, 1/25, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074099,"parameters":{"masses":[[1,2],[1,2]],"values":[-24,26],"threshold":25,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":25,\"values\":[-24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、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-20261107-r04-markov-inequality-0100","batch_id":"batch-20261014-advance-20261107-r04-markov-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-markov-inequality"],"title_zh":"Markov不等式","stem_zh":"完整正規化有限有理law、明示隨機變數與正閾值。操作=markov-negative-variable-boundary；資料={\"masses\":[[1,2],[1,2]],\"values\":[-25,27],\"threshold\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-25, 27], 否, 1/2, 1/26, Markov_not_applicable_to_signed_variable_without_transformation)","explanation_zh":"Wave6根層核對=([-25, 27], 否, 1/2, 1/26, Markov_not_applicable_to_signed_variable_without_transformation)；依完整明示資料獨立重算；Markov要求X非負almost surely、有限期望與a大於0，結論是尾機率小於等於E[X]/a；上界不等於實際尾機率；signed variable不可直接套用且禁止零閾值。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Markov不等式"]},"variant":{"family_id":"qf-mod38-markov-negative-variable-boundary","seed":202611074100,"parameters":{"masses":[[1,2],[1,2]],"values":[-25,27],"threshold":26,"domain":"Finite_rational_Markov_inequality","operation":"markov-negative-variable-boundary","semantic_template":"qf-mod38-markov-negative-variable-boundary/{\"masses\":[[1,2],[1,2]],\"threshold\":26,\"values\":[-25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}