{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0001","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/6, 1/3, 1/2], [0, 1, 4], 7/3, 26/9, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/6, 1/3, 1/2], [0, 1, 4], 7/3, 26/9, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084001,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0002","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/7, 2/7, 4/7], [0, 2, 5], 24/7, 180/49, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/7, 2/7, 4/7], [0, 2, 5], 24/7, 180/49, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084002,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0003","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/8, 1/4, 5/8], [0, 3, 6], 9/2, 9/2, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/8, 1/4, 5/8], [0, 3, 6], 9/2, 9/2, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084003,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0004","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/9, 2/9, 2/3], [0, 4, 7], 50/9, 434/81, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/9, 2/9, 2/3], [0, 4, 7], 50/9, 434/81, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084004,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0005","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/10, 1/5, 7/10], [0, 5, 8], 33/5, 156/25, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/10, 1/5, 7/10], [0, 5, 8], 33/5, 156/25, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084005,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0006","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/11, 2/11, 8/11], [0, 6, 9], 84/11, 864/121, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/11, 2/11, 8/11], [0, 6, 9], 84/11, 864/121, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084006,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0007","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/12, 1/6, 3/4], [0, 7, 10], 26/3, 145/18, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/12, 1/6, 3/4], [0, 7, 10], 26/3, 145/18, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084007,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0008","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/13, 2/13, 10/13], [0, 8, 11], 126/13, 1518/169, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/13, 2/13, 10/13], [0, 8, 11], 126/13, 1518/169, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084008,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0009","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/14, 1/7, 11/14], [0, 9, 12], 75/7, 486/49, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/14, 1/7, 11/14], [0, 9, 12], 75/7, 486/49, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084009,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0010","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/15, 2/15, 4/5], [0, 10, 13], 176/15, 2444/225, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/15, 2/15, 4/5], [0, 10, 13], 176/15, 2444/225, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084010,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0011","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/16, 1/8, 13/16], [0, 11, 14], 51/4, 189/16, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/16, 1/8, 13/16], [0, 11, 14], 51/4, 189/16, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084011,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0012","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/17, 2/17, 14/17], [0, 12, 15], 234/17, 3690/289, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/17, 2/17, 14/17], [0, 12, 15], 234/17, 3690/289, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084012,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0013","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/18, 1/9, 5/6], [0, 13, 16], 133/9, 1112/81, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/18, 1/9, 5/6], [0, 13, 16], 133/9, 1112/81, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084013,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0014","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/19, 2/19, 16/19], [0, 14, 17], 300/19, 5304/361, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/19, 2/19, 16/19], [0, 14, 17], 300/19, 5304/361, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084014,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0015","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/20, 1/10, 17/20], [0, 15, 18], 84/5, 783/50, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/20, 1/10, 17/20], [0, 15, 18], 84/5, 783/50, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084015,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0016","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/21, 2/21, 6/7], [0, 16, 19], 374/21, 7334/441, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/21, 2/21, 6/7], [0, 16, 19], 374/21, 7334/441, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084016,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0017","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/22, 1/11, 19/22], [0, 17, 20], 207/11, 2130/121, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/22, 1/11, 19/22], [0, 17, 20], 207/11, 2130/121, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084017,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0018","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/23, 2/23, 20/23], [0, 18, 21], 456/23, 9828/529, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/23, 2/23, 20/23], [0, 18, 21], 456/23, 9828/529, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084018,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0019","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/24, 1/12, 7/8], [0, 19, 22], 125/6, 176/9, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/24, 1/12, 7/8], [0, 19, 22], 125/6, 176/9, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084019,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0020","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/25, 2/25, 22/25], [0, 20, 23], 546/25, 12834/625, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/25, 2/25, 22/25], [0, 20, 23], 546/25, 12834/625, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084020,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0021","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/26, 1/13, 23/26], [0, 21, 24], 297/13, 3636/169, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/26, 1/13, 23/26], [0, 21, 24], 297/13, 3636/169, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084021,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0022","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/27, 2/27, 8/9], [0, 22, 25], 644/27, 16400/729, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/27, 2/27, 8/9], [0, 22, 25], 644/27, 16400/729, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084022,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0023","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/28, 1/14, 25/28], [0, 23, 26], 174/7, 2301/98, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/28, 1/14, 25/28], [0, 23, 26], 174/7, 2301/98, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084023,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0024","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/29, 2/29, 26/29], [0, 24, 27], 750/29, 20574/841, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/29, 2/29, 26/29], [0, 24, 27], 750/29, 20574/841, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084024,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0025","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-qualification；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1/30, 1/15, 9/10], [0, 25, 28], 403/15, 5726/225, 是, finite_mean_and_variance)","explanation_zh":"Wave6第二層核對=([1/30, 1/15, 9/10], [0, 25, 28], 403/15, 5726/225, 是, finite_mean_and_variance)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-qualification","seed":202611084025,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-qualification","semantic_template":"qf-mod39-cheb-qualification/{\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0026","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/3, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(7/3, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084026,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0027","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/7, 2, 1/7, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(24/7, 2, 1/7, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084027,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0028","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/2, 3, 1/8, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(9/2, 3, 1/8, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084028,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0029","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(50/9, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(50/9, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084029,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0030","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(33/5, 2, 1/10, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(33/5, 2, 1/10, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084030,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0031","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(84/11, 3, 1/11, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(84/11, 3, 1/11, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084031,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0032","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(26/3, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(26/3, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084032,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0033","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(126/13, 2, 1/13, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(126/13, 2, 1/13, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084033,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0034","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(75/7, 3, 1/14, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(75/7, 3, 1/14, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084034,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0035","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(176/15, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(176/15, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084035,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0036","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(51/4, 2, 1/16, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(51/4, 2, 1/16, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084036,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0037","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(234/17, 3, 1/17, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(234/17, 3, 1/17, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084037,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0038","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(133/9, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(133/9, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084038,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0039","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(300/19, 2, 1/19, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(300/19, 2, 1/19, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084039,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0040","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(84/5, 3, 1/20, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(84/5, 3, 1/20, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084040,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0041","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(374/21, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(374/21, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084041,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0042","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(207/11, 2, 1/22, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(207/11, 2, 1/22, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084042,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0043","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(456/23, 3, 1/23, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(456/23, 3, 1/23, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084043,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0044","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(125/6, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(125/6, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084044,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0045","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(546/25, 2, 1/25, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(546/25, 2, 1/25, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084045,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0046","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(297/13, 3, 1/26, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(297/13, 3, 1/26, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084046,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0047","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(644/27, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(644/27, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084047,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0048","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(174/7, 2, 1/28, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(174/7, 2, 1/28, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084048,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[2,1],\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0049","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(750/29, 3, 1/29, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(750/29, 3, 1/29, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084049,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[3,1],\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0050","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-tail-probability；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(403/15, 1, 1, exact_absolute_deviation_tail)","explanation_zh":"Wave6第二層核對=(403/15, 1, 1, exact_absolute_deviation_tail)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-tail-probability","seed":202611084050,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-tail-probability","semantic_template":"qf-mod39-cheb-tail-probability/{\"epsilon\":[1,1],\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0051","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 26/9, 26/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 26/9, 26/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084051,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0052","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/7, 180/49, 45/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/7, 180/49, 45/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084052,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0053","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/8, 9/2, 1/2, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/8, 9/2, 1/2, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084053,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0054","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 434/81, 434/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 434/81, 434/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084054,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0055","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/10, 156/25, 39/25, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/10, 156/25, 39/25, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084055,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0056","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/11, 864/121, 96/121, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/11, 864/121, 96/121, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084056,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0057","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 145/18, 145/18, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 145/18, 145/18, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084057,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0058","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/13, 1518/169, 759/338, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/13, 1518/169, 759/338, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084058,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0059","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/14, 486/49, 54/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/14, 486/49, 54/49, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084059,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0060","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2444/225, 2444/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 2444/225, 2444/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084060,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0061","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/16, 189/16, 189/64, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/16, 189/16, 189/64, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084061,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0062","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/17, 3690/289, 410/289, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/17, 3690/289, 410/289, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084062,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0063","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1112/81, 1112/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 1112/81, 1112/81, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084063,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0064","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/19, 5304/361, 1326/361, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/19, 5304/361, 1326/361, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084064,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0065","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/20, 783/50, 87/50, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/20, 783/50, 87/50, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084065,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0066","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 7334/441, 7334/441, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 7334/441, 7334/441, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084066,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0067","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/22, 2130/121, 1065/242, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/22, 2130/121, 1065/242, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084067,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0068","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/23, 9828/529, 1092/529, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/23, 9828/529, 1092/529, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084068,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0069","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 176/9, 176/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 176/9, 176/9, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084069,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0070","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/25, 12834/625, 6417/1250, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/25, 12834/625, 6417/1250, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084070,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0071","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/26, 3636/169, 404/169, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/26, 3636/169, 404/169, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084071,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0072","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 16400/729, 16400/729, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 16400/729, 16400/729, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084072,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0073","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/28, 2301/98, 2301/392, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/28, 2301/98, 2301/392, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084073,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[2,1],\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0074","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/29, 20574/841, 2286/841, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1/29, 20574/841, 2286/841, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084074,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[3,1],\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0075","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-bound-comparison；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 5726/225, 5726/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)","explanation_zh":"Wave6第二層核對=(1, 5726/225, 5726/225, 是, upper_bound_not_tail_equality_and_no_independence_needed)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-bound-comparison","seed":202611084075,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-bound-comparison","semantic_template":"qf-mod39-cheb-bound-comparison/{\"epsilon\":[1,1],\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0076","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([49/9, 16/9, 25/9], 1, 1, 1, 是, 26/9, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([49/9, 16/9, 25/9], 1, 1, 1, 是, 26/9, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084076,"parameters":{"masses":[[1,6],[2,6],[3,6]],"values":[0,1,4],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,6],[2,6],[3,6]],\"values\":[0,1,4]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0077","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([576/49, 100/49, 121/49], 4, 1/7, 1/7, 是, 45/49, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([576/49, 100/49, 121/49], 4, 1/7, 1/7, 是, 45/49, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084077,"parameters":{"masses":[[1,7],[2,7],[4,7]],"values":[0,2,5],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,7],[2,7],[4,7]],\"values\":[0,2,5]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0078","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([81/4, 9/4, 9/4], 9, 1/8, 1/8, 是, 1/2, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([81/4, 9/4, 9/4], 9, 1/8, 1/8, 是, 1/2, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084078,"parameters":{"masses":[[1,8],[2,8],[5,8]],"values":[0,3,6],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,8],[2,8],[5,8]],\"values\":[0,3,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0079","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2500/81, 196/81, 169/81], 1, 1, 1, 是, 434/81, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([2500/81, 196/81, 169/81], 1, 1, 1, 是, 434/81, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084079,"parameters":{"masses":[[1,9],[2,9],[6,9]],"values":[0,4,7],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,9],[2,9],[6,9]],\"values\":[0,4,7]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0080","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1089/25, 64/25, 49/25], 4, 1/10, 1/10, 是, 39/25, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([1089/25, 64/25, 49/25], 4, 1/10, 1/10, 是, 39/25, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084080,"parameters":{"masses":[[1,10],[2,10],[7,10]],"values":[0,5,8],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,10],[2,10],[7,10]],\"values\":[0,5,8]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0081","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([7056/121, 324/121, 225/121], 9, 1/11, 1/11, 是, 96/121, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([7056/121, 324/121, 225/121], 9, 1/11, 1/11, 是, 96/121, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084081,"parameters":{"masses":[[1,11],[2,11],[8,11]],"values":[0,6,9],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,11],[2,11],[8,11]],\"values\":[0,6,9]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0082","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([676/9, 25/9, 16/9], 1, 1, 1, 是, 145/18, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([676/9, 25/9, 16/9], 1, 1, 1, 是, 145/18, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084082,"parameters":{"masses":[[1,12],[2,12],[9,12]],"values":[0,7,10],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,12],[2,12],[9,12]],\"values\":[0,7,10]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0083","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([15876/169, 484/169, 289/169], 4, 1/13, 1/13, 是, 759/338, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([15876/169, 484/169, 289/169], 4, 1/13, 1/13, 是, 759/338, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084083,"parameters":{"masses":[[1,13],[2,13],[10,13]],"values":[0,8,11],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,13],[2,13],[10,13]],\"values\":[0,8,11]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0084","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([5625/49, 144/49, 81/49], 9, 1/14, 1/14, 是, 54/49, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([5625/49, 144/49, 81/49], 9, 1/14, 1/14, 是, 54/49, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084084,"parameters":{"masses":[[1,14],[2,14],[11,14]],"values":[0,9,12],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,14],[2,14],[11,14]],\"values\":[0,9,12]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0085","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([30976/225, 676/225, 361/225], 1, 1, 1, 是, 2444/225, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([30976/225, 676/225, 361/225], 1, 1, 1, 是, 2444/225, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084085,"parameters":{"masses":[[1,15],[2,15],[12,15]],"values":[0,10,13],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,15],[2,15],[12,15]],\"values\":[0,10,13]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0086","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2601/16, 49/16, 25/16], 4, 1/16, 1/16, 是, 189/64, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([2601/16, 49/16, 25/16], 4, 1/16, 1/16, 是, 189/64, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084086,"parameters":{"masses":[[1,16],[2,16],[13,16]],"values":[0,11,14],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,16],[2,16],[13,16]],\"values\":[0,11,14]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0087","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([54756/289, 900/289, 441/289], 9, 1/17, 1/17, 是, 410/289, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([54756/289, 900/289, 441/289], 9, 1/17, 1/17, 是, 410/289, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084087,"parameters":{"masses":[[1,17],[2,17],[14,17]],"values":[0,12,15],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,17],[2,17],[14,17]],\"values\":[0,12,15]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0088","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([17689/81, 256/81, 121/81], 1, 1, 1, 是, 1112/81, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([17689/81, 256/81, 121/81], 1, 1, 1, 是, 1112/81, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084088,"parameters":{"masses":[[1,18],[2,18],[15,18]],"values":[0,13,16],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,18],[2,18],[15,18]],\"values\":[0,13,16]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0089","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([90000/361, 1156/361, 529/361], 4, 1/19, 1/19, 是, 1326/361, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([90000/361, 1156/361, 529/361], 4, 1/19, 1/19, 是, 1326/361, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084089,"parameters":{"masses":[[1,19],[2,19],[16,19]],"values":[0,14,17],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,19],[2,19],[16,19]],\"values\":[0,14,17]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0090","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([7056/25, 81/25, 36/25], 9, 1/20, 1/20, 是, 87/50, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([7056/25, 81/25, 36/25], 9, 1/20, 1/20, 是, 87/50, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084090,"parameters":{"masses":[[1,20],[2,20],[17,20]],"values":[0,15,18],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,20],[2,20],[17,20]],\"values\":[0,15,18]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0091","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([139876/441, 1444/441, 625/441], 1, 1, 1, 是, 7334/441, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([139876/441, 1444/441, 625/441], 1, 1, 1, 是, 7334/441, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084091,"parameters":{"masses":[[1,21],[2,21],[18,21]],"values":[0,16,19],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,21],[2,21],[18,21]],\"values\":[0,16,19]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0092","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([42849/121, 400/121, 169/121], 4, 1/22, 1/22, 是, 1065/242, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([42849/121, 400/121, 169/121], 4, 1/22, 1/22, 是, 1065/242, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084092,"parameters":{"masses":[[1,22],[2,22],[19,22]],"values":[0,17,20],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,22],[2,22],[19,22]],\"values\":[0,17,20]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0093","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([207936/529, 1764/529, 729/529], 9, 1/23, 1/23, 是, 1092/529, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([207936/529, 1764/529, 729/529], 9, 1/23, 1/23, 是, 1092/529, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084093,"parameters":{"masses":[[1,23],[2,23],[20,23]],"values":[0,18,21],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,23],[2,23],[20,23]],\"values\":[0,18,21]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0094","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([15625/36, 121/36, 49/36], 1, 1, 1, 是, 176/9, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([15625/36, 121/36, 49/36], 1, 1, 1, 是, 176/9, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084094,"parameters":{"masses":[[1,24],[2,24],[21,24]],"values":[0,19,22],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,24],[2,24],[21,24]],\"values\":[0,19,22]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0095","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([298116/625, 2116/625, 841/625], 4, 1/25, 1/25, 是, 6417/1250, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([298116/625, 2116/625, 841/625], 4, 1/25, 1/25, 是, 6417/1250, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084095,"parameters":{"masses":[[1,25],[2,25],[22,25]],"values":[0,20,23],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,25],[2,25],[22,25]],\"values\":[0,20,23]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0096","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([88209/169, 576/169, 225/169], 9, 1/26, 1/26, 是, 404/169, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([88209/169, 576/169, 225/169], 9, 1/26, 1/26, 是, 404/169, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084096,"parameters":{"masses":[[1,26],[2,26],[23,26]],"values":[0,21,24],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,26],[2,26],[23,26]],\"values\":[0,21,24]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0097","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([414736/729, 2500/729, 961/729], 1, 1, 1, 是, 16400/729, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([414736/729, 2500/729, 961/729], 1, 1, 1, 是, 16400/729, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084097,"parameters":{"masses":[[1,27],[2,27],[24,27]],"values":[0,22,25],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,27],[2,27],[24,27]],\"values\":[0,22,25]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0098","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26],\"epsilon\":[2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([30276/49, 169/49, 64/49], 4, 1/28, 1/28, 是, 2301/392, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([30276/49, 169/49, 64/49], 4, 1/28, 1/28, 是, 2301/392, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084098,"parameters":{"masses":[[1,28],[2,28],[25,28]],"values":[0,23,26],"epsilon":[2,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[2,1],\"masses\":[[1,28],[2,28],[25,28]],\"values\":[0,23,26]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0099","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27],\"epsilon\":[3,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([562500/841, 2916/841, 1089/841], 9, 1/29, 1/29, 是, 2286/841, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([562500/841, 2916/841, 1089/841], 9, 1/29, 1/29, 是, 2286/841, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084099,"parameters":{"masses":[[1,29],[2,29],[26,29]],"values":[0,24,27],"epsilon":[3,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[3,1],\"masses\":[[1,29],[2,29],[26,29]],\"values\":[0,24,27]}"}},"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、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r04-chebyshev-inequality-0100","batch_id":"batch-20261014-advance-20261108-r04-chebyshev-inequality-foundations","language":"zh-Hant","source_mko_ids":["mko-chebyshev-inequality"],"title_zh":"Chebyshev不等式","stem_zh":"完整有限law、finite mean與variance及positive epsilon。操作=cheb-markov-square-derivation；資料={\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28],\"epsilon\":[1,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([162409/225, 784/225, 289/225], 1, 1, 1, 是, 5726/225, Markov_applied_to_nonnegative_squared_deviation)","explanation_zh":"Wave6第二層核對=([162409/225, 784/225, 289/225], 1, 1, 1, 是, 5726/225, Markov_applied_to_nonnegative_squared_deviation)；依完整明示資料獨立重算；P(abs(X-mu)>=epsilon)小於等於Var(X)/epsilon squared且不需要independence；對nonnegative squared deviation套Markov；bound不等於tail並保持zero-mass與zero-variance a.s.語義。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Chebyshev不等式"]},"variant":{"family_id":"qf-mod39-cheb-markov-square-derivation","seed":202611084100,"parameters":{"masses":[[1,30],[2,30],[27,30]],"values":[0,25,28],"epsilon":[1,1],"domain":"Finite_rational_Chebyshev_inequality","operation":"cheb-markov-square-derivation","semantic_template":"qf-mod39-cheb-markov-square-derivation/{\"epsilon\":[1,1],\"masses\":[[1,30],[2,30],[27,30]],\"values\":[0,25,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}