# 弱大數律基礎 · 脈衝 R07

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-20261014-advance-20261105-r07-weak-law-large-numbers-foundations · 2026-10-14 · 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](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[0,1],"variance":[1,2],"n":5,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(0, 1/2, 5, 1/10, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(0, 1/2, 5, 1/10, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0001/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 2. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[1,2],"variance":[2,3],"n":6,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(1/2, 2/3, 6, 1/9, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(1/2, 2/3, 6, 1/9, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0002/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 3. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[2,3],"variance":[3,4],"n":7,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(2/3, 3/4, 7, 3/28, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(2/3, 3/4, 7, 3/28, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0003/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 4. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[3,4],"variance":[4,5],"n":8,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(3/4, 4/5, 8, 1/10, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(3/4, 4/5, 8, 1/10, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0004/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 5. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[4,5],"variance":[5,6],"n":9,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(4/5, 5/6, 9, 5/54, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(4/5, 5/6, 9, 5/54, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0005/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 6. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[5,6],"variance":[6,7],"n":10,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(5/6, 6/7, 10, 3/35, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(5/6, 6/7, 10, 3/35, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0006/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 7. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[6,7],"variance":[7,8],"n":11,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(6/7, 7/8, 11, 7/88, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(6/7, 7/8, 11, 7/88, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0007/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 8. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[7,8],"variance":[8,9],"n":12,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(7/8, 8/9, 12, 2/27, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(7/8, 8/9, 12, 2/27, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0008/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 9. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[8,9],"variance":[9,10],"n":13,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(8/9, 9/10, 13, 9/130, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(8/9, 9/10, 13, 9/130, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0009/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 10. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[9,10],"variance":[10,11],"n":14,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(9/10, 10/11, 14, 5/77, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(9/10, 10/11, 14, 5/77, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0010/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 11. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[10,11],"variance":[11,12],"n":15,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(10/11, 11/12, 15, 11/180, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(10/11, 11/12, 15, 11/180, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0011/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 12. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[11,12],"variance":[12,13],"n":16,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(11/12, 12/13, 16, 3/52, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(11/12, 12/13, 16, 3/52, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0012/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 13. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[12,13],"variance":[13,14],"n":17,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(12/13, 13/14, 17, 13/238, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(12/13, 13/14, 17, 13/238, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0013/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 14. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[13,14],"variance":[14,15],"n":18,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(13/14, 14/15, 18, 7/135, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(13/14, 14/15, 18, 7/135, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0014/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 15. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[14,15],"variance":[15,16],"n":19,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(14/15, 15/16, 19, 15/304, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(14/15, 15/16, 19, 15/304, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0015/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 16. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[15,16],"variance":[16,17],"n":20,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(15/16, 16/17, 20, 4/85, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(15/16, 16/17, 20, 4/85, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0016/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 17. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[16,17],"variance":[17,18],"n":21,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(16/17, 17/18, 21, 17/378, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(16/17, 17/18, 21, 17/378, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0017/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 18. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[17,18],"variance":[18,19],"n":22,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(17/18, 18/19, 22, 9/209, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(17/18, 18/19, 22, 9/209, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0018/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 19. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[18,19],"variance":[19,20],"n":23,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(18/19, 19/20, 23, 19/460, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(18/19, 19/20, 23, 19/460, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0019/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 20. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[19,20],"variance":[20,21],"n":24,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(19/20, 20/21, 24, 5/126, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(19/20, 20/21, 24, 5/126, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0020/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 21. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[20,21],"variance":[21,22],"n":25,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(20/21, 21/22, 25, 21/550, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(20/21, 21/22, 25, 21/550, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0021/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 22. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[21,22],"variance":[22,23],"n":26,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(21/22, 22/23, 26, 11/299, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(21/22, 22/23, 26, 11/299, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0022/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 23. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[22,23],"variance":[23,24],"n":27,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(22/23, 23/24, 27, 23/648, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(22/23, 23/24, 27, 23/648, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0023/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 24. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[23,24],"variance":[24,25],"n":28,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(23/24, 24/25, 28, 6/175, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(23/24, 24/25, 28, 6/175, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0024/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 25. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={"mean":[24,25],"variance":[25,26],"n":29,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, variance, n, average_variance, certificate] 欄序回答。

查看答案與解釋(24/25, 25/26, 29, 25/754, independence_gives_variance_sigma_squared_over_n)

Wave5第五層核對=(24/25, 25/26, 29, 25/754, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0025/)

弱大數律 · qf-mod36-wlln-variance-average · candidate





## 26. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"n":20,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(0, 1/2, 20, 1/10, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(0, 1/2, 20, 1/10, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0026/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 27. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"n":21,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(1/2, 1/3, 21, 2/7, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(1/2, 1/3, 21, 2/7, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0027/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 28. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"n":22,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(2/3, 1/4, 22, 6/11, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(2/3, 1/4, 22, 6/11, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0028/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 29. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"n":23,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(3/4, 1/5, 23, 20/23, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(3/4, 1/5, 23, 20/23, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0029/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 30. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"n":24,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(4/5, 1/6, 24, 5/4, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(4/5, 1/6, 24, 5/4, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0030/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 31. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"n":25,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(5/6, 1/7, 25, 42/25, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(5/6, 1/7, 25, 42/25, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0031/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 32. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"n":26,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(6/7, 1/8, 26, 28/13, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(6/7, 1/8, 26, 28/13, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0032/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 33. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"n":27,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(7/8, 1/9, 27, 8/3, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(7/8, 1/9, 27, 8/3, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0033/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 34. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"n":28,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(8/9, 1/10, 28, 45/14, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(8/9, 1/10, 28, 45/14, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0034/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 35. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"n":29,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(9/10, 1/11, 29, 110/29, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(9/10, 1/11, 29, 110/29, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0035/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 36. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"n":30,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(10/11, 1/12, 30, 22/5, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(10/11, 1/12, 30, 22/5, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0036/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 37. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"n":31,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(11/12, 1/13, 31, 156/31, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(11/12, 1/13, 31, 156/31, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0037/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 38. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"n":32,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(12/13, 1/14, 32, 91/16, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(12/13, 1/14, 32, 91/16, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0038/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 39. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"n":33,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(13/14, 1/15, 33, 70/11, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(13/14, 1/15, 33, 70/11, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0039/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 40. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"n":34,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(14/15, 1/16, 34, 120/17, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(14/15, 1/16, 34, 120/17, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0040/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 41. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"n":35,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(15/16, 1/17, 35, 272/35, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(15/16, 1/17, 35, 272/35, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0041/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 42. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"n":36,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(16/17, 1/18, 36, 17/2, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(16/17, 1/18, 36, 17/2, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0042/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 43. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"n":37,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(17/18, 1/19, 37, 342/37, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(17/18, 1/19, 37, 342/37, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0043/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 44. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"n":38,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(18/19, 1/20, 38, 10, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(18/19, 1/20, 38, 10, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0044/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 45. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"n":39,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(19/20, 1/21, 39, 140/13, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(19/20, 1/21, 39, 140/13, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0045/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 46. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"n":40,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(20/21, 1/22, 40, 231/20, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(20/21, 1/22, 40, 231/20, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0046/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 47. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"n":41,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(21/22, 1/23, 41, 506/41, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(21/22, 1/23, 41, 506/41, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0047/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 48. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"n":42,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(22/23, 1/24, 42, 92/7, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(22/23, 1/24, 42, 92/7, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0048/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 49. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"n":43,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(23/24, 1/25, 43, 600/43, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(23/24, 1/25, 43, 600/43, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0049/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 50. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"n":44,"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [mean, epsilon, n, probability_upper_bound, conditional_upper_bound_valid, certificate] 欄序回答。

此欄是條件於明示IID前提的Chebyshev機率上界，可大於1；不是事件機率值，也不是新增Lean證明。

查看答案與解釋(24/25, 1/26, 44, 325/22, 是, probability_upper_bound_not_finite_n_equality)

Wave5第五層核對=(24/25, 1/26, 44, 325/22, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0050/)

弱大數律 · qf-mod36-wlln-chebyshev-bound · candidate





## 51. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"delta":[1,10],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/2, 1/10, 21, 2/21, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/2, 1/10, 21, 2/21, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0051/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 52. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"delta":[1,11],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/3, 1/11, 67, 6/67, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/3, 1/11, 67, 6/67, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0052/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 53. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"delta":[1,12],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/4, 1/12, 145, 12/145, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/4, 1/12, 145, 12/145, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0053/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 54. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"delta":[1,13],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/5, 1/13, 261, 20/261, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/5, 1/13, 261, 20/261, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0054/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 55. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"delta":[1,14],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/6, 1/14, 421, 30/421, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/6, 1/14, 421, 30/421, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0055/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 56. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"delta":[1,15],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/7, 1/15, 631, 42/631, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/7, 1/15, 631, 42/631, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0056/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 57. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"delta":[1,16],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/8, 1/16, 897, 56/897, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/8, 1/16, 897, 56/897, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0057/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 58. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"delta":[1,17],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/9, 1/17, 1225, 72/1225, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/9, 1/17, 1225, 72/1225, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0058/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 59. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"delta":[1,18],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/10, 1/18, 1621, 90/1621, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/10, 1/18, 1621, 90/1621, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0059/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 60. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"delta":[1,19],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/11, 1/19, 2091, 110/2091, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/11, 1/19, 2091, 110/2091, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0060/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 61. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"delta":[1,20],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/12, 1/20, 2641, 132/2641, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/12, 1/20, 2641, 132/2641, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0061/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 62. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"delta":[1,21],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/13, 1/21, 3277, 156/3277, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/13, 1/21, 3277, 156/3277, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0062/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 63. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"delta":[1,22],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/14, 1/22, 4005, 182/4005, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/14, 1/22, 4005, 182/4005, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0063/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 64. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"delta":[1,23],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/15, 1/23, 4831, 210/4831, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/15, 1/23, 4831, 210/4831, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0064/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 65. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"delta":[1,24],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/16, 1/24, 5761, 240/5761, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/16, 1/24, 5761, 240/5761, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0065/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 66. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"delta":[1,25],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/17, 1/25, 6801, 272/6801, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/17, 1/25, 6801, 272/6801, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0066/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 67. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"delta":[1,26],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/18, 1/26, 7957, 306/7957, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/18, 1/26, 7957, 306/7957, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0067/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 68. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"delta":[1,27],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/19, 1/27, 9235, 342/9235, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/19, 1/27, 9235, 342/9235, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0068/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 69. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"delta":[1,28],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/20, 1/28, 10641, 380/10641, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/20, 1/28, 10641, 380/10641, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0069/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 70. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"delta":[1,29],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/21, 1/29, 12181, 420/12181, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/21, 1/29, 12181, 420/12181, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0070/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 71. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"delta":[1,30],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/22, 1/30, 13861, 462/13861, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/22, 1/30, 13861, 462/13861, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0071/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 72. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"delta":[1,31],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/23, 1/31, 15687, 506/15687, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/23, 1/31, 15687, 506/15687, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0072/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 73. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"delta":[1,32],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/24, 1/32, 17665, 552/17665, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/24, 1/32, 17665, 552/17665, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0073/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 74. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"delta":[1,33],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/25, 1/33, 19801, 600/19801, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/25, 1/33, 19801, 600/19801, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0074/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 75. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"delta":[1,34],"iid_certificate":"symbolic_all_finite_subfamilies"}。請依 [epsilon, delta, N, chebyshev_bound_at_N, strict_delta_tail, certificate] 欄序回答。

IID標記是明示的全序列前提，不由有限模擬或欄序資料證成；嚴格delta界須對所有n≥N成立。

查看答案與解釋(1/26, 1/34, 22101, 650/22101, 是, forall_n_ge_N_monotone_Chebyshev_tail)

Wave5第五層核對=(1/26, 1/34, 22101, 650/22101, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0075/)

弱大數律 · qf-mod36-wlln-epsilon-delta-witness · candidate





## 76. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"prefix_sample_means":[[1,2],[2,3],[3,4]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(0, 1/2, [1/2, 2/3, 3/4], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(0, 1/2, [1/2, 2/3, 3/4], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0076/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 77. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"prefix_sample_means":[[2,3],[3,4],[4,5]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(1/2, 1/3, [2/3, 3/4, 4/5], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(1/2, 1/3, [2/3, 3/4, 4/5], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0077/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 78. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"prefix_sample_means":[[3,4],[4,5],[5,6]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(2/3, 1/4, [3/4, 4/5, 5/6], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(2/3, 1/4, [3/4, 4/5, 5/6], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0078/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 79. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"prefix_sample_means":[[4,5],[5,6],[6,7]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(3/4, 1/5, [4/5, 5/6, 6/7], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(3/4, 1/5, [4/5, 5/6, 6/7], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0079/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 80. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"prefix_sample_means":[[5,6],[6,7],[7,8]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(4/5, 1/6, [5/6, 6/7, 7/8], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(4/5, 1/6, [5/6, 6/7, 7/8], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0080/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 81. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"prefix_sample_means":[[6,7],[7,8],[8,9]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(5/6, 1/7, [6/7, 7/8, 8/9], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(5/6, 1/7, [6/7, 7/8, 8/9], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0081/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 82. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"prefix_sample_means":[[7,8],[8,9],[9,10]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(6/7, 1/8, [7/8, 8/9, 9/10], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(6/7, 1/8, [7/8, 8/9, 9/10], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0082/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 83. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"prefix_sample_means":[[8,9],[9,10],[10,11]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(7/8, 1/9, [8/9, 9/10, 10/11], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(7/8, 1/9, [8/9, 9/10, 10/11], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0083/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 84. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"prefix_sample_means":[[9,10],[10,11],[11,12]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(8/9, 1/10, [9/10, 10/11, 11/12], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(8/9, 1/10, [9/10, 10/11, 11/12], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0084/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 85. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"prefix_sample_means":[[10,11],[11,12],[12,13]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(9/10, 1/11, [10/11, 11/12, 12/13], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(9/10, 1/11, [10/11, 11/12, 12/13], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0085/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 86. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"prefix_sample_means":[[11,12],[12,13],[13,14]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(10/11, 1/12, [11/12, 12/13, 13/14], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(10/11, 1/12, [11/12, 12/13, 13/14], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0086/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 87. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"prefix_sample_means":[[12,13],[13,14],[14,15]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(11/12, 1/13, [12/13, 13/14, 14/15], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(11/12, 1/13, [12/13, 13/14, 14/15], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0087/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 88. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"prefix_sample_means":[[13,14],[14,15],[15,16]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(12/13, 1/14, [13/14, 14/15, 15/16], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(12/13, 1/14, [13/14, 14/15, 15/16], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0088/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 89. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"prefix_sample_means":[[14,15],[15,16],[16,17]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(13/14, 1/15, [14/15, 15/16, 16/17], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(13/14, 1/15, [14/15, 15/16, 16/17], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0089/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 90. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"prefix_sample_means":[[15,16],[16,17],[17,18]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(14/15, 1/16, [15/16, 16/17, 17/18], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(14/15, 1/16, [15/16, 16/17, 17/18], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0090/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 91. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"prefix_sample_means":[[16,17],[17,18],[18,19]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0091/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 92. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"prefix_sample_means":[[17,18],[18,19],[19,20]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(16/17, 1/18, [17/18, 18/19, 19/20], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(16/17, 1/18, [17/18, 18/19, 19/20], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0092/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 93. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"prefix_sample_means":[[18,19],[19,20],[20,21]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(17/18, 1/19, [18/19, 19/20, 20/21], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(17/18, 1/19, [18/19, 19/20, 20/21], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0093/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 94. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"prefix_sample_means":[[19,20],[20,21],[21,22]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(18/19, 1/20, [19/20, 20/21, 21/22], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(18/19, 1/20, [19/20, 20/21, 21/22], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0094/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 95. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"prefix_sample_means":[[20,21],[21,22],[22,23]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(19/20, 1/21, [20/21, 21/22, 22/23], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(19/20, 1/21, [20/21, 21/22, 22/23], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0095/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 96. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"prefix_sample_means":[[21,22],[22,23],[23,24]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(20/21, 1/22, [21/22, 22/23, 23/24], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(20/21, 1/22, [21/22, 22/23, 23/24], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0096/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 97. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"prefix_sample_means":[[22,23],[23,24],[24,25]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(21/22, 1/23, [22/23, 23/24, 24/25], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(21/22, 1/23, [22/23, 23/24, 24/25], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0097/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 98. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"prefix_sample_means":[[23,24],[24,25],[25,26]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(22/23, 1/24, [23/24, 24/25, 25/26], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(22/23, 1/24, [23/24, 24/25, 25/26], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0098/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 99. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"prefix_sample_means":[[24,25],[25,26],[26,27]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(23/24, 1/25, [24/25, 25/26, 26/27], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(23/24, 1/25, [24/25, 25/26, 26/27], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0099/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate





## 100. 弱大數律

IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"prefix_sample_means":[[25,26],[26,27],[27,28]],"iid_certificate":"finite_simulation_only"}。請依 [mean, epsilon, prefix_sample_means, sufficient, boundary] 欄序回答。

查看答案與解釋(24/25, 1/26, [25/26, 26/27, 27/28], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)

Wave5第五層核對=(24/25, 1/26, [25/26, 26/27, 27/28], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261014-advance-20261105-r07-weak-law-large-numbers-0100/)

弱大數律 · qf-mod36-wlln-finite-simulation-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations/validation-report.json)