{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0001","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[0,1,3],\"masses\":[[1,4],[1,4],[1,4]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)","explanation_zh":"結構基礎核對=([0, 1, 3], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227001,"parameters":{"outcomes":[0,1,3],"masses":[[1,4],[1,4],[1,4]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,4]],\"outcomes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0002","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[1,2,4],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([1, 2, 4], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227002,"parameters":{"outcomes":[1,2,4],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0003","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[2,3,5],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 5], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([2, 3, 5], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227003,"parameters":{"outcomes":[2,3,5],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0004","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[3,4,6],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([3, 4, 6], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([3, 4, 6], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227004,"parameters":{"outcomes":[3,4,6],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0005","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[4,5,7],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([4, 5, 7], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([4, 5, 7], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227005,"parameters":{"outcomes":[4,5,7],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[4,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0006","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[5,6,8],\"masses\":[[1,4],[1,4],[1,4]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([5, 6, 8], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)","explanation_zh":"結構基礎核對=([5, 6, 8], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227006,"parameters":{"outcomes":[5,6,8],"masses":[[1,4],[1,4],[1,4]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,4]],\"outcomes\":[5,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0007","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[6,7,9],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([6, 7, 9], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([6, 7, 9], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227007,"parameters":{"outcomes":[6,7,9],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[6,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0008","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[7,8,10],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([7, 8, 10], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([7, 8, 10], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227008,"parameters":{"outcomes":[7,8,10],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[7,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0009","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[8,9,11],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([8, 9, 11], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([8, 9, 11], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227009,"parameters":{"outcomes":[8,9,11],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[8,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0010","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[9,10,12],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([9, 10, 12], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([9, 10, 12], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227010,"parameters":{"outcomes":[9,10,12],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[9,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0011","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[10,11,13],\"masses\":[[1,4],[1,4],[1,4]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 13], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)","explanation_zh":"結構基礎核對=([10, 11, 13], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227011,"parameters":{"outcomes":[10,11,13],"masses":[[1,4],[1,4],[1,4]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,4]],\"outcomes\":[10,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0012","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[11,12,14],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([11, 12, 14], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([11, 12, 14], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227012,"parameters":{"outcomes":[11,12,14],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[11,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0013","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[12,13,15],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([12, 13, 15], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([12, 13, 15], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227013,"parameters":{"outcomes":[12,13,15],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[12,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0014","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[13,14,16],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([13, 14, 16], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([13, 14, 16], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227014,"parameters":{"outcomes":[13,14,16],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[13,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0015","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[14,15,17],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([14, 15, 17], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([14, 15, 17], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227015,"parameters":{"outcomes":[14,15,17],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[14,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0016","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[15,16,18],\"masses\":[[1,4],[1,4],[1,4]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([15, 16, 18], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)","explanation_zh":"結構基礎核對=([15, 16, 18], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227016,"parameters":{"outcomes":[15,16,18],"masses":[[1,4],[1,4],[1,4]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,4]],\"outcomes\":[15,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0017","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[16,17,19],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([16, 17, 19], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([16, 17, 19], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227017,"parameters":{"outcomes":[16,17,19],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[16,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0018","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[17,18,20],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([17, 18, 20], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([17, 18, 20], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227018,"parameters":{"outcomes":[17,18,20],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[17,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0019","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[18,19,21],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([18, 19, 21], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([18, 19, 21], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227019,"parameters":{"outcomes":[18,19,21],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[18,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0020","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[19,20,22],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([19, 20, 22], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([19, 20, 22], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227020,"parameters":{"outcomes":[19,20,22],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[19,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0021","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[20,21,23],\"masses\":[[1,4],[1,4],[1,4]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 23], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)","explanation_zh":"結構基礎核對=([20, 21, 23], [1/4, 1/4, 1/4], 是, 3/4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227021,"parameters":{"outcomes":[20,21,23],"masses":[[1,4],[1,4],[1,4]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,4]],\"outcomes\":[20,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0022","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[21,22,24],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([21, 22, 24], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([21, 22, 24], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227022,"parameters":{"outcomes":[21,22,24],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[21,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0023","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[22,23,25],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([22, 23, 25], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([22, 23, 25], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227023,"parameters":{"outcomes":[22,23,25],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[22,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0024","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[23,24,26],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([23, 24, 26], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([23, 24, 26], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227024,"parameters":{"outcomes":[23,24,26],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[23,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0025","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pmf-qualification；資料={\"outcomes\":[24,25,27],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,nonnegative,sum,normalized,qualified] 欄序回答。","answer":{"kind":"expression","value":"([24, 25, 27], [1/4, 1/4, 1/2], 是, 1, 是, 是)","explanation_zh":"結構基礎核對=([24, 25, 27], [1/4, 1/4, 1/2], 是, 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pmf-qualification","seed":202610227025,"parameters":{"outcomes":[24,25,27],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pmf-qualification","semantic_template":"qf-str22-distribution-pmf-qualification/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[24,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0026","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[0,1,3],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[0,3]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [1/4, 1/4, 1/2], [0, 3], 3/4)","explanation_zh":"結構基礎核對=([0, 1, 3], [1/4, 1/4, 1/2], [0, 3], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227026,"parameters":{"outcomes":[0,1,3],"masses":[[1,4],[1,4],[1,2]],"event":[0,3],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[0,3],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0027","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[1,2,4],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[1,4]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [1/4, 1/4, 1/2], [1, 4], 3/4)","explanation_zh":"結構基礎核對=([1, 2, 4], [1/4, 1/4, 1/2], [1, 4], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227027,"parameters":{"outcomes":[1,2,4],"masses":[[1,4],[1,4],[1,2]],"event":[1,4],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[1,4],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0028","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[2,3,5],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[2,5]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 5], [1/4, 1/4, 1/2], [2, 5], 3/4)","explanation_zh":"結構基礎核對=([2, 3, 5], [1/4, 1/4, 1/2], [2, 5], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227028,"parameters":{"outcomes":[2,3,5],"masses":[[1,4],[1,4],[1,2]],"event":[2,5],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[2,5],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0029","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[3,4,6],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[3,6]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([3, 4, 6], [1/4, 1/4, 1/2], [3, 6], 3/4)","explanation_zh":"結構基礎核對=([3, 4, 6], [1/4, 1/4, 1/2], [3, 6], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227029,"parameters":{"outcomes":[3,4,6],"masses":[[1,4],[1,4],[1,2]],"event":[3,6],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[3,6],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0030","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[4,5,7],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[4,7]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([4, 5, 7], [1/4, 1/4, 1/2], [4, 7], 3/4)","explanation_zh":"結構基礎核對=([4, 5, 7], [1/4, 1/4, 1/2], [4, 7], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227030,"parameters":{"outcomes":[4,5,7],"masses":[[1,4],[1,4],[1,2]],"event":[4,7],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[4,7],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[4,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0031","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[5,6,8],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[5,8]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([5, 6, 8], [1/4, 1/4, 1/2], [5, 8], 3/4)","explanation_zh":"結構基礎核對=([5, 6, 8], [1/4, 1/4, 1/2], [5, 8], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227031,"parameters":{"outcomes":[5,6,8],"masses":[[1,4],[1,4],[1,2]],"event":[5,8],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[5,8],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[5,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0032","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[6,7,9],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[6,9]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([6, 7, 9], [1/4, 1/4, 1/2], [6, 9], 3/4)","explanation_zh":"結構基礎核對=([6, 7, 9], [1/4, 1/4, 1/2], [6, 9], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227032,"parameters":{"outcomes":[6,7,9],"masses":[[1,4],[1,4],[1,2]],"event":[6,9],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[6,9],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[6,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0033","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[7,8,10],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[7,10]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([7, 8, 10], [1/4, 1/4, 1/2], [7, 10], 3/4)","explanation_zh":"結構基礎核對=([7, 8, 10], [1/4, 1/4, 1/2], [7, 10], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227033,"parameters":{"outcomes":[7,8,10],"masses":[[1,4],[1,4],[1,2]],"event":[7,10],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[7,10],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[7,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0034","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[8,9,11],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[8,11]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([8, 9, 11], [1/4, 1/4, 1/2], [8, 11], 3/4)","explanation_zh":"結構基礎核對=([8, 9, 11], [1/4, 1/4, 1/2], [8, 11], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227034,"parameters":{"outcomes":[8,9,11],"masses":[[1,4],[1,4],[1,2]],"event":[8,11],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[8,11],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[8,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0035","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[9,10,12],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[9,12]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([9, 10, 12], [1/4, 1/4, 1/2], [9, 12], 3/4)","explanation_zh":"結構基礎核對=([9, 10, 12], [1/4, 1/4, 1/2], [9, 12], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227035,"parameters":{"outcomes":[9,10,12],"masses":[[1,4],[1,4],[1,2]],"event":[9,12],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[9,12],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[9,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0036","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[10,11,13],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[10,13]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 13], [1/4, 1/4, 1/2], [10, 13], 3/4)","explanation_zh":"結構基礎核對=([10, 11, 13], [1/4, 1/4, 1/2], [10, 13], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227036,"parameters":{"outcomes":[10,11,13],"masses":[[1,4],[1,4],[1,2]],"event":[10,13],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[10,13],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[10,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0037","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[11,12,14],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[11,14]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([11, 12, 14], [1/4, 1/4, 1/2], [11, 14], 3/4)","explanation_zh":"結構基礎核對=([11, 12, 14], [1/4, 1/4, 1/2], [11, 14], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227037,"parameters":{"outcomes":[11,12,14],"masses":[[1,4],[1,4],[1,2]],"event":[11,14],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[11,14],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[11,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0038","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[12,13,15],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[12,15]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([12, 13, 15], [1/4, 1/4, 1/2], [12, 15], 3/4)","explanation_zh":"結構基礎核對=([12, 13, 15], [1/4, 1/4, 1/2], [12, 15], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227038,"parameters":{"outcomes":[12,13,15],"masses":[[1,4],[1,4],[1,2]],"event":[12,15],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[12,15],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[12,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0039","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[13,14,16],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[13,16]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([13, 14, 16], [1/4, 1/4, 1/2], [13, 16], 3/4)","explanation_zh":"結構基礎核對=([13, 14, 16], [1/4, 1/4, 1/2], [13, 16], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227039,"parameters":{"outcomes":[13,14,16],"masses":[[1,4],[1,4],[1,2]],"event":[13,16],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[13,16],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[13,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0040","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[14,15,17],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[14,17]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([14, 15, 17], [1/4, 1/4, 1/2], [14, 17], 3/4)","explanation_zh":"結構基礎核對=([14, 15, 17], [1/4, 1/4, 1/2], [14, 17], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227040,"parameters":{"outcomes":[14,15,17],"masses":[[1,4],[1,4],[1,2]],"event":[14,17],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[14,17],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[14,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0041","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[15,16,18],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[15,18]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([15, 16, 18], [1/4, 1/4, 1/2], [15, 18], 3/4)","explanation_zh":"結構基礎核對=([15, 16, 18], [1/4, 1/4, 1/2], [15, 18], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227041,"parameters":{"outcomes":[15,16,18],"masses":[[1,4],[1,4],[1,2]],"event":[15,18],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[15,18],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[15,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0042","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[16,17,19],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[16,19]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([16, 17, 19], [1/4, 1/4, 1/2], [16, 19], 3/4)","explanation_zh":"結構基礎核對=([16, 17, 19], [1/4, 1/4, 1/2], [16, 19], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227042,"parameters":{"outcomes":[16,17,19],"masses":[[1,4],[1,4],[1,2]],"event":[16,19],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[16,19],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[16,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0043","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[17,18,20],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[17,20]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([17, 18, 20], [1/4, 1/4, 1/2], [17, 20], 3/4)","explanation_zh":"結構基礎核對=([17, 18, 20], [1/4, 1/4, 1/2], [17, 20], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227043,"parameters":{"outcomes":[17,18,20],"masses":[[1,4],[1,4],[1,2]],"event":[17,20],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[17,20],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[17,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0044","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[18,19,21],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[18,21]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([18, 19, 21], [1/4, 1/4, 1/2], [18, 21], 3/4)","explanation_zh":"結構基礎核對=([18, 19, 21], [1/4, 1/4, 1/2], [18, 21], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227044,"parameters":{"outcomes":[18,19,21],"masses":[[1,4],[1,4],[1,2]],"event":[18,21],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[18,21],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[18,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0045","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[19,20,22],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[19,22]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([19, 20, 22], [1/4, 1/4, 1/2], [19, 22], 3/4)","explanation_zh":"結構基礎核對=([19, 20, 22], [1/4, 1/4, 1/2], [19, 22], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227045,"parameters":{"outcomes":[19,20,22],"masses":[[1,4],[1,4],[1,2]],"event":[19,22],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[19,22],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[19,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0046","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[20,21,23],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[20,23]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 23], [1/4, 1/4, 1/2], [20, 23], 3/4)","explanation_zh":"結構基礎核對=([20, 21, 23], [1/4, 1/4, 1/2], [20, 23], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227046,"parameters":{"outcomes":[20,21,23],"masses":[[1,4],[1,4],[1,2]],"event":[20,23],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[20,23],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[20,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0047","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[21,22,24],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[21,24]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([21, 22, 24], [1/4, 1/4, 1/2], [21, 24], 3/4)","explanation_zh":"結構基礎核對=([21, 22, 24], [1/4, 1/4, 1/2], [21, 24], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227047,"parameters":{"outcomes":[21,22,24],"masses":[[1,4],[1,4],[1,2]],"event":[21,24],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[21,24],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[21,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0048","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[22,23,25],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[22,25]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([22, 23, 25], [1/4, 1/4, 1/2], [22, 25], 3/4)","explanation_zh":"結構基礎核對=([22, 23, 25], [1/4, 1/4, 1/2], [22, 25], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227048,"parameters":{"outcomes":[22,23,25],"masses":[[1,4],[1,4],[1,2]],"event":[22,25],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[22,25],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[22,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0049","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[23,24,26],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[23,26]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([23, 24, 26], [1/4, 1/4, 1/2], [23, 26], 3/4)","explanation_zh":"結構基礎核對=([23, 24, 26], [1/4, 1/4, 1/2], [23, 26], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227049,"parameters":{"outcomes":[23,24,26],"masses":[[1,4],[1,4],[1,2]],"event":[23,26],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[23,26],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[23,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0050","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-event-probability；資料={\"outcomes\":[24,25,27],\"masses\":[[1,4],[1,4],[1,2]],\"event\":[24,27]}。請依 [outcomes,masses,event,event_probability] 欄序回答。","answer":{"kind":"expression","value":"([24, 25, 27], [1/4, 1/4, 1/2], [24, 27], 3/4)","explanation_zh":"結構基礎核對=([24, 25, 27], [1/4, 1/4, 1/2], [24, 27], 3/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-event-probability","seed":202610227050,"parameters":{"outcomes":[24,25,27],"masses":[[1,4],[1,4],[1,2]],"event":[24,27],"domain":"Exact_finite_discrete_pmf","operation":"distribution-event-probability","semantic_template":"qf-str22-distribution-event-probability/{\"event\":[24,27],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[24,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0051","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[0,1,3],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [1/4, 1/4, 1/2], 7/4)","explanation_zh":"結構基礎核對=([0, 1, 3], [1/4, 1/4, 1/2], 7/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227051,"parameters":{"outcomes":[0,1,3],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0052","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[1,2,4],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [1/4, 1/4, 1/2], 11/4)","explanation_zh":"結構基礎核對=([1, 2, 4], [1/4, 1/4, 1/2], 11/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227052,"parameters":{"outcomes":[1,2,4],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0053","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[2,3,5],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 5], [1/4, 1/4, 1/2], 15/4)","explanation_zh":"結構基礎核對=([2, 3, 5], [1/4, 1/4, 1/2], 15/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227053,"parameters":{"outcomes":[2,3,5],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0054","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[3,4,6],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([3, 4, 6], [1/4, 1/4, 1/2], 19/4)","explanation_zh":"結構基礎核對=([3, 4, 6], [1/4, 1/4, 1/2], 19/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227054,"parameters":{"outcomes":[3,4,6],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0055","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[4,5,7],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([4, 5, 7], [1/4, 1/4, 1/2], 23/4)","explanation_zh":"結構基礎核對=([4, 5, 7], [1/4, 1/4, 1/2], 23/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227055,"parameters":{"outcomes":[4,5,7],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[4,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0056","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[5,6,8],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([5, 6, 8], [1/4, 1/4, 1/2], 27/4)","explanation_zh":"結構基礎核對=([5, 6, 8], [1/4, 1/4, 1/2], 27/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227056,"parameters":{"outcomes":[5,6,8],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[5,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0057","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[6,7,9],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([6, 7, 9], [1/4, 1/4, 1/2], 31/4)","explanation_zh":"結構基礎核對=([6, 7, 9], [1/4, 1/4, 1/2], 31/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227057,"parameters":{"outcomes":[6,7,9],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[6,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0058","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[7,8,10],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([7, 8, 10], [1/4, 1/4, 1/2], 35/4)","explanation_zh":"結構基礎核對=([7, 8, 10], [1/4, 1/4, 1/2], 35/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227058,"parameters":{"outcomes":[7,8,10],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[7,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0059","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[8,9,11],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([8, 9, 11], [1/4, 1/4, 1/2], 39/4)","explanation_zh":"結構基礎核對=([8, 9, 11], [1/4, 1/4, 1/2], 39/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227059,"parameters":{"outcomes":[8,9,11],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[8,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0060","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[9,10,12],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([9, 10, 12], [1/4, 1/4, 1/2], 43/4)","explanation_zh":"結構基礎核對=([9, 10, 12], [1/4, 1/4, 1/2], 43/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227060,"parameters":{"outcomes":[9,10,12],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[9,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0061","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[10,11,13],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 13], [1/4, 1/4, 1/2], 47/4)","explanation_zh":"結構基礎核對=([10, 11, 13], [1/4, 1/4, 1/2], 47/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227061,"parameters":{"outcomes":[10,11,13],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[10,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0062","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[11,12,14],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([11, 12, 14], [1/4, 1/4, 1/2], 51/4)","explanation_zh":"結構基礎核對=([11, 12, 14], [1/4, 1/4, 1/2], 51/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227062,"parameters":{"outcomes":[11,12,14],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[11,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0063","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[12,13,15],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([12, 13, 15], [1/4, 1/4, 1/2], 55/4)","explanation_zh":"結構基礎核對=([12, 13, 15], [1/4, 1/4, 1/2], 55/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227063,"parameters":{"outcomes":[12,13,15],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[12,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0064","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[13,14,16],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([13, 14, 16], [1/4, 1/4, 1/2], 59/4)","explanation_zh":"結構基礎核對=([13, 14, 16], [1/4, 1/4, 1/2], 59/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227064,"parameters":{"outcomes":[13,14,16],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[13,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0065","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[14,15,17],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([14, 15, 17], [1/4, 1/4, 1/2], 63/4)","explanation_zh":"結構基礎核對=([14, 15, 17], [1/4, 1/4, 1/2], 63/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227065,"parameters":{"outcomes":[14,15,17],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[14,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0066","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[15,16,18],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([15, 16, 18], [1/4, 1/4, 1/2], 67/4)","explanation_zh":"結構基礎核對=([15, 16, 18], [1/4, 1/4, 1/2], 67/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227066,"parameters":{"outcomes":[15,16,18],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[15,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0067","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[16,17,19],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([16, 17, 19], [1/4, 1/4, 1/2], 71/4)","explanation_zh":"結構基礎核對=([16, 17, 19], [1/4, 1/4, 1/2], 71/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227067,"parameters":{"outcomes":[16,17,19],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[16,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0068","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[17,18,20],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([17, 18, 20], [1/4, 1/4, 1/2], 75/4)","explanation_zh":"結構基礎核對=([17, 18, 20], [1/4, 1/4, 1/2], 75/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227068,"parameters":{"outcomes":[17,18,20],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[17,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0069","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[18,19,21],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([18, 19, 21], [1/4, 1/4, 1/2], 79/4)","explanation_zh":"結構基礎核對=([18, 19, 21], [1/4, 1/4, 1/2], 79/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227069,"parameters":{"outcomes":[18,19,21],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[18,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0070","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[19,20,22],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([19, 20, 22], [1/4, 1/4, 1/2], 83/4)","explanation_zh":"結構基礎核對=([19, 20, 22], [1/4, 1/4, 1/2], 83/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227070,"parameters":{"outcomes":[19,20,22],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[19,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0071","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[20,21,23],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 23], [1/4, 1/4, 1/2], 87/4)","explanation_zh":"結構基礎核對=([20, 21, 23], [1/4, 1/4, 1/2], 87/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227071,"parameters":{"outcomes":[20,21,23],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[20,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0072","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[21,22,24],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([21, 22, 24], [1/4, 1/4, 1/2], 91/4)","explanation_zh":"結構基礎核對=([21, 22, 24], [1/4, 1/4, 1/2], 91/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227072,"parameters":{"outcomes":[21,22,24],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[21,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0073","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[22,23,25],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([22, 23, 25], [1/4, 1/4, 1/2], 95/4)","explanation_zh":"結構基礎核對=([22, 23, 25], [1/4, 1/4, 1/2], 95/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227073,"parameters":{"outcomes":[22,23,25],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[22,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0074","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[23,24,26],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([23, 24, 26], [1/4, 1/4, 1/2], 99/4)","explanation_zh":"結構基礎核對=([23, 24, 26], [1/4, 1/4, 1/2], 99/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227074,"parameters":{"outcomes":[23,24,26],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[23,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0075","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-expectation；資料={\"outcomes\":[24,25,27],\"masses\":[[1,4],[1,4],[1,2]]}。請依 [outcomes,masses,expectation] 欄序回答。","answer":{"kind":"expression","value":"([24, 25, 27], [1/4, 1/4, 1/2], 103/4)","explanation_zh":"結構基礎核對=([24, 25, 27], [1/4, 1/4, 1/2], 103/4)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-expectation","seed":202610227075,"parameters":{"outcomes":[24,25,27],"masses":[[1,4],[1,4],[1,2]],"domain":"Exact_finite_discrete_pmf","operation":"distribution-expectation","semantic_template":"qf-str22-distribution-expectation/{\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[24,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0076","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[0,1,3],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([0, 1, 3], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227076,"parameters":{"outcomes":[0,1,3],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0077","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[1,2,4],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([1, 2, 4], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227077,"parameters":{"outcomes":[1,2,4],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0078","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[2,3,5],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 5], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([2, 3, 5], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227078,"parameters":{"outcomes":[2,3,5],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[2,3,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0079","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[3,4,6],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([3, 4, 6], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([3, 4, 6], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227079,"parameters":{"outcomes":[3,4,6],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[3,4,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0080","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[4,5,7],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([4, 5, 7], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([4, 5, 7], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227080,"parameters":{"outcomes":[4,5,7],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[4,5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0081","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[5,6,8],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([5, 6, 8], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([5, 6, 8], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227081,"parameters":{"outcomes":[5,6,8],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[5,6,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0082","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[6,7,9],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([6, 7, 9], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([6, 7, 9], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227082,"parameters":{"outcomes":[6,7,9],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[6,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0083","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[7,8,10],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([7, 8, 10], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([7, 8, 10], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227083,"parameters":{"outcomes":[7,8,10],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[7,8,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0084","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[8,9,11],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([8, 9, 11], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([8, 9, 11], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227084,"parameters":{"outcomes":[8,9,11],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[8,9,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0085","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[9,10,12],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([9, 10, 12], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([9, 10, 12], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227085,"parameters":{"outcomes":[9,10,12],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[9,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0086","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[10,11,13],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 13], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([10, 11, 13], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227086,"parameters":{"outcomes":[10,11,13],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[10,11,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0087","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[11,12,14],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([11, 12, 14], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([11, 12, 14], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227087,"parameters":{"outcomes":[11,12,14],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[11,12,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0088","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[12,13,15],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([12, 13, 15], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([12, 13, 15], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227088,"parameters":{"outcomes":[12,13,15],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[12,13,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0089","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[13,14,16],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([13, 14, 16], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([13, 14, 16], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227089,"parameters":{"outcomes":[13,14,16],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[13,14,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0090","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[14,15,17],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([14, 15, 17], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([14, 15, 17], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227090,"parameters":{"outcomes":[14,15,17],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[14,15,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0091","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[15,16,18],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([15, 16, 18], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([15, 16, 18], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227091,"parameters":{"outcomes":[15,16,18],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[15,16,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0092","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[16,17,19],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([16, 17, 19], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([16, 17, 19], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227092,"parameters":{"outcomes":[16,17,19],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[16,17,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0093","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[17,18,20],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([17, 18, 20], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([17, 18, 20], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227093,"parameters":{"outcomes":[17,18,20],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[17,18,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0094","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[18,19,21],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([18, 19, 21], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([18, 19, 21], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227094,"parameters":{"outcomes":[18,19,21],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[18,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0095","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[19,20,22],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([19, 20, 22], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([19, 20, 22], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227095,"parameters":{"outcomes":[19,20,22],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[19,20,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0096","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[20,21,23],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 23], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([20, 21, 23], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227096,"parameters":{"outcomes":[20,21,23],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[20,21,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0097","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[21,22,24],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([21, 22, 24], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([21, 22, 24], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227097,"parameters":{"outcomes":[21,22,24],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[21,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0098","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[22,23,25],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[1,2,1]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([22, 23, 25], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])","explanation_zh":"結構基礎核對=([22, 23, 25], [1/4, 1/4, 1/2], [1, 2, 1], [[1, 3/4], [2, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227098,"parameters":{"outcomes":[22,23,25],"masses":[[1,4],[1,4],[1,2]],"images":[1,2,1],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[1,2,1],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[22,23,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0099","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[23,24,26],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[2,0,2]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([23, 24, 26], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])","explanation_zh":"結構基礎核對=([23, 24, 26], [1/4, 1/4, 1/2], [2, 0, 2], [[0, 1/4], [2, 3/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227099,"parameters":{"outcomes":[23,24,26],"masses":[[1,4],[1,4],[1,2]],"images":[2,0,2],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[2,0,2],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[23,24,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r07-finite-discrete-probability-distribution-0100","batch_id":"batch-20261013-advance-20261022-r07-finite-discrete-probability-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-discrete-probability-distribution"],"title_zh":"有限離散PMF","stem_zh":"有限離散精確PMF。操作=distribution-pushforward；資料={\"outcomes\":[24,25,27],\"masses\":[[1,4],[1,4],[1,2]],\"images\":[0,1,0]}。請依 [outcomes,masses,images,pushforward_rows] 欄序回答。","answer":{"kind":"expression","value":"([24, 25, 27], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])","explanation_zh":"結構基礎核對=([24, 25, 27], [1/4, 1/4, 1/2], [0, 1, 0], [[0, 3/4], [1, 1/4]])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；質量非負且精確和為1；數學分布不是資料擬合證據。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限離散PMF"]},"variant":{"family_id":"qf-str22-distribution-pushforward","seed":202610227100,"parameters":{"outcomes":[24,25,27],"masses":[[1,4],[1,4],[1,2]],"images":[0,1,0],"domain":"Exact_finite_discrete_pmf","operation":"distribution-pushforward","semantic_template":"qf-str22-distribution-pushforward/{\"images\":[0,1,0],\"masses\":[[1,4],[1,4],[1,2]],\"outcomes\":[24,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}