有限值IID強大數律基礎 · 脈衝 R02
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261118-r02-strong-law-large-numbers-finite-valued-iid-foundations · 2026-10-15 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
欄序與來源綁定資料
1. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-2, 1/2], [-1, 1/2]], -3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-2, 1/2], [-1, 1/2]], -3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
2. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-1, 1/2], [0, 1/2]], -1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-1, 1/2], [0, 1/2]], -1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
3. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[0, 1/2], [1, 1/2]], 1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[0, 1/2], [1, 1/2]], 1/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
4. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[1, 1/2], [2, 1/2]], 3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[1, 1/2], [2, 1/2]], 3/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
5. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[2, 1/2], [3, 1/2]], 5/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[2, 1/2], [3, 1/2]], 5/2, 1/4, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
6. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-2,-1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-2, 1/3], [-1, 2/3]], -4/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-2, 1/3], [-1, 2/3]], -4/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
7. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-1,0],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-1, 1/3], [0, 2/3]], -1/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-1, 1/3], [0, 2/3]], -1/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
8. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[0,1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[0, 1/3], [1, 2/3]], 2/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[0, 1/3], [1, 2/3]], 2/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
9. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[1,2],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[1, 1/3], [2, 2/3]], 5/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[1, 1/3], [2, 2/3]], 5/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
10. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[2,3],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[2, 1/3], [3, 2/3]], 8/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[2, 1/3], [3, 2/3]], 8/3, 2/9, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
11. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-2,-1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-2, 1/4], [-1, 3/4]], -5/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-2, 1/4], [-1, 3/4]], -5/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
12. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-1,0],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-1, 1/4], [0, 3/4]], -1/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-1, 1/4], [0, 3/4]], -1/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
13. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[0,1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[0, 1/4], [1, 3/4]], 3/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[0, 1/4], [1, 3/4]], 3/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
14. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[1,2],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[1, 1/4], [2, 3/4]], 7/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[1, 1/4], [2, 3/4]], 7/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
15. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[2,3],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[2, 1/4], [3, 3/4]], 11/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[2, 1/4], [3, 3/4]], 11/4, 3/16, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
16. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-2,-1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-2, 2/5], [-1, 3/5]], -7/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-2, 2/5], [-1, 3/5]], -7/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
17. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-1,0],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-1, 2/5], [0, 3/5]], -2/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-1, 2/5], [0, 3/5]], -2/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
18. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[0,1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[0, 2/5], [1, 3/5]], 3/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[0, 2/5], [1, 3/5]], 3/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
19. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[1,2],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[1, 2/5], [2, 3/5]], 8/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[1, 2/5], [2, 3/5]], 8/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
20. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[2,3],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[2, 2/5], [3, 3/5]], 13/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[2, 2/5], [3, 3/5]], 13/5, 6/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
21. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-2,-1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-2, 1/5], [-1, 4/5]], -6/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-2, 1/5], [-1, 4/5]], -6/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
22. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[-1,0],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[-1, 1/5], [0, 4/5]], -1/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[-1, 1/5], [0, 4/5]], -1/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
23. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[0,1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[0, 1/5], [1, 4/5]], 4/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[0, 1/5], [1, 4/5]], 4/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
24. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[1,2],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[1, 1/5], [2, 4/5]], 9/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[1, 1/5], [2, 4/5]], 9/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
25. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-process-law-qualification；資料={"values":[2,3],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid"}。請依 [law_rows, mean, variance, declared_process_certificate, named_theorem_conclusion, conditional_application_qualified] 欄序回答。
finite law可含零變異數；a.s.結論依宣告的無限IID前提與named theorem，不由有限資料推出。
查看答案與解釋
([[2, 1/5], [3, 4/5]], 14/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)
Wave6第十二層核對=([[2, 1/5], [3, 4/5]], 14/5, 4/25, infinite_iid, P(lim_sample_mean=mu)=1, 是)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-process-law-qualification · candidate
26. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[-2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-2], -3/2, -2, 1/2, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-2], -3/2, -2, 1/2, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
27. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[0,-1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0, -1], -1/2, -1/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0, -1], -1/2, -1/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
28. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[0,1,0]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0, 1, 0], 1/2, 1/3, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0, 1, 0], 1/2, 1/3, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
29. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[2,1,2,1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2, 1, 2, 1], 3/2, 3/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2, 1, 2, 1], 3/2, 3/2, 0, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
30. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","observations":[2,3,2,3,2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2, 3, 2, 3, 2], 5/2, 12/5, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2, 3, 2, 3, 2], 5/2, 12/5, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
31. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-2,-1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[-1,-2,-1,-2,-1,-2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-1, -2, -1, -2, -1, -2], -4/3, -3/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-1, -2, -1, -2, -1, -2], -4/3, -3/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
32. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-1,0],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[-1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-1], -1/3, -1, 2/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-1], -1/3, -1, 2/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
33. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[0,1],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[1,0]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([1, 0], 2/3, 1/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([1, 0], 2/3, 1/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
34. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[1,2],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[1,2,1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([1, 2, 1], 5/3, 4/3, 1/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([1, 2, 1], 5/3, 4/3, 1/3, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
35. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[2,3],"probabilities":[[1,3],[2,3]],"process_certificate":"infinite_iid","observations":[3,2,3,2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([3, 2, 3, 2], 8/3, 5/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([3, 2, 3, 2], 8/3, 5/2, 1/6, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
36. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-2,-1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[-2,-1,-2,-1,-2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-2, -1, -2, -1, -2], -5/4, -8/5, 7/20, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-2, -1, -2, -1, -2], -5/4, -8/5, 7/20, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
37. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-1,0],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[0,-1,0,-1,0,-1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0, -1, 0, -1, 0, -1], -1/4, -1/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0, -1, 0, -1, 0, -1], -1/4, -1/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
38. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[0,1],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[0]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0], 3/4, 0, 3/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0], 3/4, 0, 3/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
39. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[1,2],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[2,1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2, 1], 7/4, 3/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2, 1], 7/4, 3/2, 1/4, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
40. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[2,3],"probabilities":[[1,4],[3,4]],"process_certificate":"infinite_iid","observations":[2,3,2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2, 3, 2], 11/4, 7/3, 5/12, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2, 3, 2], 11/4, 7/3, 5/12, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
41. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-2,-1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[-1,-2,-1,-2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-1, -2, -1, -2], -7/5, -3/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-1, -2, -1, -2], -7/5, -3/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
42. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-1,0],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[-1,0,-1,0,-1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-1, 0, -1, 0, -1], -2/5, -3/5, 1/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-1, 0, -1, 0, -1], -2/5, -3/5, 1/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
43. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[0,1],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[1,0,1,0,1,0]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([1, 0, 1, 0, 1, 0], 3/5, 1/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([1, 0, 1, 0, 1, 0], 3/5, 1/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
44. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[1,2],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([1], 8/5, 1, 3/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([1], 8/5, 1, 3/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
45. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[2,3],"probabilities":[[2,5],[3,5]],"process_certificate":"infinite_iid","observations":[3,2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([3, 2], 13/5, 5/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([3, 2], 13/5, 5/2, 1/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
46. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-2,-1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[-2,-1,-2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([-2, -1, -2], -6/5, -5/3, 7/15, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([-2, -1, -2], -6/5, -5/3, 7/15, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
47. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[-1,0],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[0,-1,0,-1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0, -1, 0, -1], -1/5, -1/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0, -1, 0, -1], -1/5, -1/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
48. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[0,1],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[0,1,0,1,0]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([0, 1, 0, 1, 0], 4/5, 2/5, 2/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([0, 1, 0, 1, 0], 4/5, 2/5, 2/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
49. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[1,2],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[2,1,2,1,2,1]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2, 1, 2, 1, 2, 1], 9/5, 3/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2, 1, 2, 1, 2, 1], 9/5, 3/2, 3/10, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
50. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-prefix-sample-mean；資料={"values":[2,3],"probabilities":[[1,5],[4,5]],"process_certificate":"infinite_iid","observations":[2]}。請依 [observations, common_mean, prefix_sample_mean, absolute_error, evidence_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
查看答案與解釋
([2], 14/5, 2, 4/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)
Wave6第十二層核對=([2], 14/5, 2, 4/5, fixed_prefix_only, 否, finite_prefix_does_not_prove_almost_sure_convergence)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-prefix-sample-mean · candidate
51. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(1, -3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(1, -3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
52. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(1, -1/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(1, -1/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
53. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(1, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(1, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
54. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(1, 3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(1, 3/2, 1/3, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
55. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":1,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(1, 5/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(1, 5/2, 1/2, 2, 1, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
56. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(2, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(2, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
57. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(2, -1/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(2, -1/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
58. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(2, 1/2, 1/2, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(2, 1/2, 1/2, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
59. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(2, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(2, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
60. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":2,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(2, 5/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(2, 5/2, 1/3, 2, 1/2, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
61. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(3, -3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(3, -3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
62. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(3, -1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(3, -1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
63. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(3, 1/2, 1/3, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(3, 1/2, 1/3, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
64. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(3, 3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(3, 3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
65. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(3, 5/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(3, 5/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
66. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(4, -3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(4, -3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
67. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(4, -1/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(4, -1/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
68. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(4, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(4, 1/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
69. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(4, 3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(4, 3/2, 1/3, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
70. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":4,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(4, 5/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(4, 5/2, 1/2, 2, 1/8, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
71. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-2,-1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(5, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(5, -3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
72. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(5, -1/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(5, -1/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
73. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[0,1],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[2,4]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(5, 1/2, 1/2, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(5, 1/2, 1/2, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
74. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[3,5]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(5, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(5, 3/2, 3/5, 0, 0, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
75. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[2,3],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5,"epsilon":[1,3]}。請依 [n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary] 欄序回答。
count含全部偏離的joint words，包括機率零的word；probability另依law加權。事件用≥epsilon，不是>epsilon。
查看答案與解釋
(5, 5/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)
Wave6第十二層核對=(5, 5/2, 1/3, 2, 1/16, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-fixed-n-deviation · candidate
76. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"nonfinite_support","model":{"support_kind":"countably_infinite","moment_status":"integrable"}}。請依 [mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)
Wave6第十二層核對=(nonfinite_support, countably_infinite, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
77. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"nonfinite_support","model":{"support_kind":"countably_infinite","moment_status":"unknown"}}。請依 [mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(nonfinite_support, countably_infinite, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)
Wave6第十二層核對=(nonfinite_support, countably_infinite, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
78. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"nonfinite_support","model":{"support_kind":"continuous","moment_status":"integrable"}}。請依 [mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(nonfinite_support, continuous, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)
Wave6第十二層核對=(nonfinite_support, continuous, integrable, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
79. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"nonfinite_support","model":{"support_kind":"continuous","moment_status":"unknown"}}。請依 [mode, support_kind, moment_status, this_finite_valued_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(nonfinite_support, continuous, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)
Wave6第十二層核對=(nonfinite_support, continuous, unknown, 否, outside_finite_valued_scope_not_a_counterexample_to_general_SLLN)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
80. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[2,3],"probabilities_a":[[1,2],[1,2]],"values_b":[2,3],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
81. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[-2,-1],"probabilities":[[1,3],[2,3]],"observations":[-2,-1,-1]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [-2, -1, -1], -4/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [-2, -1, -1], -4/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
82. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[-1,0],"probabilities":[[1,3],[2,3]],"target":8}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, -1/3, 8, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, -1/3, 8, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
83. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[0,1],"probabilities_a":[[1,3],[2,3]],"values_b":[0,1],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
84. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[1,2],"probabilities":[[1,3],[2,3]],"observations":[1,2,1]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [1, 2, 1], 5/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [1, 2, 1], 5/3, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
85. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[2,3],"probabilities":[[1,3],[2,3]],"target":11}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, 8/3, 11, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, 8/3, 11, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
86. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[-2,-1],"probabilities_a":[[1,4],[3,4]],"values_b":[-2,-1],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
87. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[-1,0],"probabilities":[[1,4],[3,4]],"observations":[-1,0,0]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [-1, 0, 0], -1/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [-1, 0, 0], -1/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
88. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[0,1],"probabilities":[[1,4],[3,4]],"target":14}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, 3/4, 14, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, 3/4, 14, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
89. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[1,2],"probabilities_a":[[1,4],[3,4]],"values_b":[1,2],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
90. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[2,3],"probabilities":[[1,4],[3,4]],"observations":[2,3,2]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [2, 3, 2], 11/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [2, 3, 2], 11/4, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
91. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[-2,-1],"probabilities":[[2,5],[3,5]],"target":17}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, -7/5, 17, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, -7/5, 17, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
92. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[-1,0],"probabilities_a":[[2,5],[3,5]],"values_b":[-1,0],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
93. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[0,1],"probabilities":[[2,5],[3,5]],"observations":[0,1,1]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [0, 1, 1], 3/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [0, 1, 1], 3/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
94. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[1,2],"probabilities":[[2,5],[3,5]],"target":20}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, 8/5, 20, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, 8/5, 20, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
95. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[2,3],"probabilities_a":[[2,5],[3,5]],"values_b":[2,3],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
96. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[-2,-1],"probabilities":[[1,5],[4,5]],"observations":[-2,-1,-2]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [-2, -1, -2], -6/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [-2, -1, -2], -6/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
97. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[-1,0],"probabilities":[[1,5],[4,5]],"target":23}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, -1/5, 23, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, -1/5, 23, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
98. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"non_iid","model":{"values_a":[0,1],"probabilities_a":[[1,5],[4,5]],"values_b":[0,1],"probabilities_b":[[1,7],[6,7]]}}。請依 [mode, identical_marginals, this_finite_valued_IID_theorem_applicable, scope] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)
Wave6第十二層核對=(non_iid, 否, 否, finite_valued_IID_SLLN_not_applicable_not_general_failure)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
99. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"finite_prefix","model":{"values":[1,2],"probabilities":[[1,5],[4,5]],"observations":[1,2,2]}}。請依 [mode, observations, common_mean, infinite_process_or_limit_proof_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(finite_prefix, [1, 2, 2], 9/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)
Wave6第十二層核對=(finite_prefix, [1, 2, 2], 9/5, 否, finite_prefix_cannot_establish_infinite_process_or_a.s._limit)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
100. 有限值IID強大數律
無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-scope-boundary；資料={"mode":"wrong_target","model":{"values":[2,3],"probabilities":[[1,5],[4,5]],"target":26}}。請依 [mode, common_mean, proposed_target, target_equals_common_mean, proposed_target_claim, boundary] 欄序回答。
四種mode為4/5/6/5欄；nonfinite_support與non-IID是本節範圍不適用，不是一般SLLN反例。
查看答案與解釋
(wrong_target, 14/5, 26, 否, 否, SLLN_target_is_common_expectation)
Wave6第十二層核對=(wrong_target, 14/5, 26, 否, 否, SLLN_target_is_common_expectation)；依完整明示資料獨立重算；固定prefix mean與deviation event只屬fixed-n audit；non-IID/nonfinite-support是scoped theorem不適用，finite prefix不證a.s. convergence。
本題逐步詳解（AI 二次覆核）
有限值IID強大數律 · qf-mod49-slln-scope-boundary · candidate
原始題目 JSONL · 驗收報告