# 標準常態分布基礎 · 脈衝 R04

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-20261114-r04-standard-normal-distribution-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](https://ocme.evemisslab.com/data/i18n/question-output-protocols.json)



## 1. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[1,2]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(1/2, (2*pi)^(-1/2)*exp(-1/8), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(1/2, (2*pi)^(-1/2)*exp(-1/8), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0001/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 2. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-2,3]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-2/3, (2*pi)^(-1/2)*exp(-2/9), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-2/3, (2*pi)^(-1/2)*exp(-2/9), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0002/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 3. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[3,4]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(3/4, (2*pi)^(-1/2)*exp(-9/32), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(3/4, (2*pi)^(-1/2)*exp(-9/32), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0003/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 4. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-4,5]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-4/5, (2*pi)^(-1/2)*exp(-8/25), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-4/5, (2*pi)^(-1/2)*exp(-8/25), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0004/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 5. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[5,6]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(5/6, (2*pi)^(-1/2)*exp(-25/72), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(5/6, (2*pi)^(-1/2)*exp(-25/72), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0005/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 6. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-6,7]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-6/7, (2*pi)^(-1/2)*exp(-18/49), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-6/7, (2*pi)^(-1/2)*exp(-18/49), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0006/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 7. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[7,8]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(7/8, (2*pi)^(-1/2)*exp(-49/128), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(7/8, (2*pi)^(-1/2)*exp(-49/128), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0007/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 8. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-8,9]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-8/9, (2*pi)^(-1/2)*exp(-32/81), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-8/9, (2*pi)^(-1/2)*exp(-32/81), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0008/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 9. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[9,10]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(9/10, (2*pi)^(-1/2)*exp(-81/200), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(9/10, (2*pi)^(-1/2)*exp(-81/200), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0009/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 10. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-10,11]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-10/11, (2*pi)^(-1/2)*exp(-50/121), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-10/11, (2*pi)^(-1/2)*exp(-50/121), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0010/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 11. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[11,12]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(11/12, (2*pi)^(-1/2)*exp(-121/288), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(11/12, (2*pi)^(-1/2)*exp(-121/288), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0011/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 12. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-12,13]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-12/13, (2*pi)^(-1/2)*exp(-72/169), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-12/13, (2*pi)^(-1/2)*exp(-72/169), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0012/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 13. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[13,14]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(13/14, (2*pi)^(-1/2)*exp(-169/392), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(13/14, (2*pi)^(-1/2)*exp(-169/392), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0013/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 14. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-14,15]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-14/15, (2*pi)^(-1/2)*exp(-98/225), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-14/15, (2*pi)^(-1/2)*exp(-98/225), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0014/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 15. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[15,16]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(15/16, (2*pi)^(-1/2)*exp(-225/512), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(15/16, (2*pi)^(-1/2)*exp(-225/512), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0015/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 16. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-16,17]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-16/17, (2*pi)^(-1/2)*exp(-128/289), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-16/17, (2*pi)^(-1/2)*exp(-128/289), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0016/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 17. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[17,18]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(17/18, (2*pi)^(-1/2)*exp(-289/648), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(17/18, (2*pi)^(-1/2)*exp(-289/648), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0017/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 18. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-18,19]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-18/19, (2*pi)^(-1/2)*exp(-162/361), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-18/19, (2*pi)^(-1/2)*exp(-162/361), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0018/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 19. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[19,20]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(19/20, (2*pi)^(-1/2)*exp(-361/800), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(19/20, (2*pi)^(-1/2)*exp(-361/800), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0019/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 20. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-20,21]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-20/21, (2*pi)^(-1/2)*exp(-200/441), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-20/21, (2*pi)^(-1/2)*exp(-200/441), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0020/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 21. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[21,22]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(21/22, (2*pi)^(-1/2)*exp(-441/968), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(21/22, (2*pi)^(-1/2)*exp(-441/968), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0021/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 22. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-22,23]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-22/23, (2*pi)^(-1/2)*exp(-242/529), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-22/23, (2*pi)^(-1/2)*exp(-242/529), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0022/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 23. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[23,24]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(23/24, (2*pi)^(-1/2)*exp(-529/1152), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(23/24, (2*pi)^(-1/2)*exp(-529/1152), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0023/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 24. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[-24,25]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(-24/25, (2*pi)^(-1/2)*exp(-288/625), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(-24/25, (2*pi)^(-1/2)*exp(-288/625), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0024/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 25. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-symbolic-density；資料={"x":[25,26]}。請依 [x, symbolic_density, density_law, normalization_scope] 欄序回答。

查看答案與解釋(25/26, (2*pi)^(-1/2)*exp(-625/1352), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)

Wave6第八層核對=(25/26, (2*pi)^(-1/2)*exp(-625/1352), phi(x)=(2*pi)^(-1/2)*exp(-x^2/2), normalization_is_a_named_Gaussian_integral_fact_not_a_finite_evaluation)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0025/)

標準常態分布 · qf-mod45-normaldist-symbolic-density · candidate





## 26. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[1,2]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(1/2, -1/2, (2*pi)^(-1/2)*exp(-1/8), (2*pi)^(-1/2)*exp(-1/8), 是, phi(x)/phi(0)=exp(-1/8), evenness_follows_from_x_squared)

Wave6第八層核對=(1/2, -1/2, (2*pi)^(-1/2)*exp(-1/8), (2*pi)^(-1/2)*exp(-1/8), 是, phi(x)/phi(0)=exp(-1/8), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0026/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 27. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-2,3]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-2/3, 2/3, (2*pi)^(-1/2)*exp(-2/9), (2*pi)^(-1/2)*exp(-2/9), 是, phi(x)/phi(0)=exp(-2/9), evenness_follows_from_x_squared)

Wave6第八層核對=(-2/3, 2/3, (2*pi)^(-1/2)*exp(-2/9), (2*pi)^(-1/2)*exp(-2/9), 是, phi(x)/phi(0)=exp(-2/9), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0027/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 28. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[3,4]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(3/4, -3/4, (2*pi)^(-1/2)*exp(-9/32), (2*pi)^(-1/2)*exp(-9/32), 是, phi(x)/phi(0)=exp(-9/32), evenness_follows_from_x_squared)

Wave6第八層核對=(3/4, -3/4, (2*pi)^(-1/2)*exp(-9/32), (2*pi)^(-1/2)*exp(-9/32), 是, phi(x)/phi(0)=exp(-9/32), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0028/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 29. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-4,5]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-4/5, 4/5, (2*pi)^(-1/2)*exp(-8/25), (2*pi)^(-1/2)*exp(-8/25), 是, phi(x)/phi(0)=exp(-8/25), evenness_follows_from_x_squared)

Wave6第八層核對=(-4/5, 4/5, (2*pi)^(-1/2)*exp(-8/25), (2*pi)^(-1/2)*exp(-8/25), 是, phi(x)/phi(0)=exp(-8/25), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0029/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 30. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[5,6]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(5/6, -5/6, (2*pi)^(-1/2)*exp(-25/72), (2*pi)^(-1/2)*exp(-25/72), 是, phi(x)/phi(0)=exp(-25/72), evenness_follows_from_x_squared)

Wave6第八層核對=(5/6, -5/6, (2*pi)^(-1/2)*exp(-25/72), (2*pi)^(-1/2)*exp(-25/72), 是, phi(x)/phi(0)=exp(-25/72), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0030/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 31. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-6,7]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-6/7, 6/7, (2*pi)^(-1/2)*exp(-18/49), (2*pi)^(-1/2)*exp(-18/49), 是, phi(x)/phi(0)=exp(-18/49), evenness_follows_from_x_squared)

Wave6第八層核對=(-6/7, 6/7, (2*pi)^(-1/2)*exp(-18/49), (2*pi)^(-1/2)*exp(-18/49), 是, phi(x)/phi(0)=exp(-18/49), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0031/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 32. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[7,8]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(7/8, -7/8, (2*pi)^(-1/2)*exp(-49/128), (2*pi)^(-1/2)*exp(-49/128), 是, phi(x)/phi(0)=exp(-49/128), evenness_follows_from_x_squared)

Wave6第八層核對=(7/8, -7/8, (2*pi)^(-1/2)*exp(-49/128), (2*pi)^(-1/2)*exp(-49/128), 是, phi(x)/phi(0)=exp(-49/128), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0032/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 33. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-8,9]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-8/9, 8/9, (2*pi)^(-1/2)*exp(-32/81), (2*pi)^(-1/2)*exp(-32/81), 是, phi(x)/phi(0)=exp(-32/81), evenness_follows_from_x_squared)

Wave6第八層核對=(-8/9, 8/9, (2*pi)^(-1/2)*exp(-32/81), (2*pi)^(-1/2)*exp(-32/81), 是, phi(x)/phi(0)=exp(-32/81), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0033/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 34. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[9,10]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(9/10, -9/10, (2*pi)^(-1/2)*exp(-81/200), (2*pi)^(-1/2)*exp(-81/200), 是, phi(x)/phi(0)=exp(-81/200), evenness_follows_from_x_squared)

Wave6第八層核對=(9/10, -9/10, (2*pi)^(-1/2)*exp(-81/200), (2*pi)^(-1/2)*exp(-81/200), 是, phi(x)/phi(0)=exp(-81/200), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0034/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 35. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-10,11]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-10/11, 10/11, (2*pi)^(-1/2)*exp(-50/121), (2*pi)^(-1/2)*exp(-50/121), 是, phi(x)/phi(0)=exp(-50/121), evenness_follows_from_x_squared)

Wave6第八層核對=(-10/11, 10/11, (2*pi)^(-1/2)*exp(-50/121), (2*pi)^(-1/2)*exp(-50/121), 是, phi(x)/phi(0)=exp(-50/121), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0035/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 36. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[11,12]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(11/12, -11/12, (2*pi)^(-1/2)*exp(-121/288), (2*pi)^(-1/2)*exp(-121/288), 是, phi(x)/phi(0)=exp(-121/288), evenness_follows_from_x_squared)

Wave6第八層核對=(11/12, -11/12, (2*pi)^(-1/2)*exp(-121/288), (2*pi)^(-1/2)*exp(-121/288), 是, phi(x)/phi(0)=exp(-121/288), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0036/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 37. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-12,13]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-12/13, 12/13, (2*pi)^(-1/2)*exp(-72/169), (2*pi)^(-1/2)*exp(-72/169), 是, phi(x)/phi(0)=exp(-72/169), evenness_follows_from_x_squared)

Wave6第八層核對=(-12/13, 12/13, (2*pi)^(-1/2)*exp(-72/169), (2*pi)^(-1/2)*exp(-72/169), 是, phi(x)/phi(0)=exp(-72/169), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0037/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 38. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[13,14]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(13/14, -13/14, (2*pi)^(-1/2)*exp(-169/392), (2*pi)^(-1/2)*exp(-169/392), 是, phi(x)/phi(0)=exp(-169/392), evenness_follows_from_x_squared)

Wave6第八層核對=(13/14, -13/14, (2*pi)^(-1/2)*exp(-169/392), (2*pi)^(-1/2)*exp(-169/392), 是, phi(x)/phi(0)=exp(-169/392), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0038/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 39. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-14,15]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-14/15, 14/15, (2*pi)^(-1/2)*exp(-98/225), (2*pi)^(-1/2)*exp(-98/225), 是, phi(x)/phi(0)=exp(-98/225), evenness_follows_from_x_squared)

Wave6第八層核對=(-14/15, 14/15, (2*pi)^(-1/2)*exp(-98/225), (2*pi)^(-1/2)*exp(-98/225), 是, phi(x)/phi(0)=exp(-98/225), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0039/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 40. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[15,16]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(15/16, -15/16, (2*pi)^(-1/2)*exp(-225/512), (2*pi)^(-1/2)*exp(-225/512), 是, phi(x)/phi(0)=exp(-225/512), evenness_follows_from_x_squared)

Wave6第八層核對=(15/16, -15/16, (2*pi)^(-1/2)*exp(-225/512), (2*pi)^(-1/2)*exp(-225/512), 是, phi(x)/phi(0)=exp(-225/512), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0040/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 41. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-16,17]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-16/17, 16/17, (2*pi)^(-1/2)*exp(-128/289), (2*pi)^(-1/2)*exp(-128/289), 是, phi(x)/phi(0)=exp(-128/289), evenness_follows_from_x_squared)

Wave6第八層核對=(-16/17, 16/17, (2*pi)^(-1/2)*exp(-128/289), (2*pi)^(-1/2)*exp(-128/289), 是, phi(x)/phi(0)=exp(-128/289), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0041/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 42. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[17,18]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(17/18, -17/18, (2*pi)^(-1/2)*exp(-289/648), (2*pi)^(-1/2)*exp(-289/648), 是, phi(x)/phi(0)=exp(-289/648), evenness_follows_from_x_squared)

Wave6第八層核對=(17/18, -17/18, (2*pi)^(-1/2)*exp(-289/648), (2*pi)^(-1/2)*exp(-289/648), 是, phi(x)/phi(0)=exp(-289/648), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0042/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 43. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-18,19]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-18/19, 18/19, (2*pi)^(-1/2)*exp(-162/361), (2*pi)^(-1/2)*exp(-162/361), 是, phi(x)/phi(0)=exp(-162/361), evenness_follows_from_x_squared)

Wave6第八層核對=(-18/19, 18/19, (2*pi)^(-1/2)*exp(-162/361), (2*pi)^(-1/2)*exp(-162/361), 是, phi(x)/phi(0)=exp(-162/361), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0043/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 44. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[19,20]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(19/20, -19/20, (2*pi)^(-1/2)*exp(-361/800), (2*pi)^(-1/2)*exp(-361/800), 是, phi(x)/phi(0)=exp(-361/800), evenness_follows_from_x_squared)

Wave6第八層核對=(19/20, -19/20, (2*pi)^(-1/2)*exp(-361/800), (2*pi)^(-1/2)*exp(-361/800), 是, phi(x)/phi(0)=exp(-361/800), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0044/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 45. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-20,21]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-20/21, 20/21, (2*pi)^(-1/2)*exp(-200/441), (2*pi)^(-1/2)*exp(-200/441), 是, phi(x)/phi(0)=exp(-200/441), evenness_follows_from_x_squared)

Wave6第八層核對=(-20/21, 20/21, (2*pi)^(-1/2)*exp(-200/441), (2*pi)^(-1/2)*exp(-200/441), 是, phi(x)/phi(0)=exp(-200/441), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0045/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 46. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[21,22]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(21/22, -21/22, (2*pi)^(-1/2)*exp(-441/968), (2*pi)^(-1/2)*exp(-441/968), 是, phi(x)/phi(0)=exp(-441/968), evenness_follows_from_x_squared)

Wave6第八層核對=(21/22, -21/22, (2*pi)^(-1/2)*exp(-441/968), (2*pi)^(-1/2)*exp(-441/968), 是, phi(x)/phi(0)=exp(-441/968), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0046/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 47. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-22,23]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-22/23, 22/23, (2*pi)^(-1/2)*exp(-242/529), (2*pi)^(-1/2)*exp(-242/529), 是, phi(x)/phi(0)=exp(-242/529), evenness_follows_from_x_squared)

Wave6第八層核對=(-22/23, 22/23, (2*pi)^(-1/2)*exp(-242/529), (2*pi)^(-1/2)*exp(-242/529), 是, phi(x)/phi(0)=exp(-242/529), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0047/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 48. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[23,24]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(23/24, -23/24, (2*pi)^(-1/2)*exp(-529/1152), (2*pi)^(-1/2)*exp(-529/1152), 是, phi(x)/phi(0)=exp(-529/1152), evenness_follows_from_x_squared)

Wave6第八層核對=(23/24, -23/24, (2*pi)^(-1/2)*exp(-529/1152), (2*pi)^(-1/2)*exp(-529/1152), 是, phi(x)/phi(0)=exp(-529/1152), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0048/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 49. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[-24,25]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(-24/25, 24/25, (2*pi)^(-1/2)*exp(-288/625), (2*pi)^(-1/2)*exp(-288/625), 是, phi(x)/phi(0)=exp(-288/625), evenness_follows_from_x_squared)

Wave6第八層核對=(-24/25, 24/25, (2*pi)^(-1/2)*exp(-288/625), (2*pi)^(-1/2)*exp(-288/625), 是, phi(x)/phi(0)=exp(-288/625), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0049/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 50. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-evenness-ratio；資料={"x":[25,26]}。請依 [x, negative_x, density_at_x, density_at_negative_x, even, density_ratio, certificate] 欄序回答。

查看答案與解釋(25/26, -25/26, (2*pi)^(-1/2)*exp(-625/1352), (2*pi)^(-1/2)*exp(-625/1352), 是, phi(x)/phi(0)=exp(-625/1352), evenness_follows_from_x_squared)

Wave6第八層核對=(25/26, -25/26, (2*pi)^(-1/2)*exp(-625/1352), (2*pi)^(-1/2)*exp(-625/1352), 是, phi(x)/phi(0)=exp(-625/1352), evenness_follows_from_x_squared)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0050/)

標準常態分布 · qf-mod45-normaldist-evenness-ratio · candidate





## 51. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-12}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-12, Phi(12)=1-Phi(-12), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-12, Phi(12)=1-Phi(-12), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0051/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 52. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-11}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-11, Phi(11)=1-Phi(-11), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-11, Phi(11)=1-Phi(-11), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0052/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 53. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-10}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-10, Phi(10)=1-Phi(-10), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-10, Phi(10)=1-Phi(-10), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0053/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 54. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-9}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-9, Phi(9)=1-Phi(-9), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-9, Phi(9)=1-Phi(-9), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0054/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 55. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-8}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-8, Phi(8)=1-Phi(-8), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-8, Phi(8)=1-Phi(-8), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0055/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 56. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-7}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-7, Phi(7)=1-Phi(-7), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-7, Phi(7)=1-Phi(-7), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0056/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 57. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-6}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-6, Phi(6)=1-Phi(-6), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-6, Phi(6)=1-Phi(-6), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0057/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 58. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-5}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-5, Phi(5)=1-Phi(-5), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-5, Phi(5)=1-Phi(-5), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0058/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 59. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-4}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-4, Phi(4)=1-Phi(-4), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-4, Phi(4)=1-Phi(-4), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0059/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 60. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-3}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-3, Phi(3)=1-Phi(-3), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-3, Phi(3)=1-Phi(-3), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0060/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 61. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-2}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-2, Phi(2)=1-Phi(-2), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-2, Phi(2)=1-Phi(-2), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0061/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 62. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":-1}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(-1, Phi(1)=1-Phi(-1), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(-1, Phi(1)=1-Phi(-1), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0062/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 63. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":0}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(0, Phi(0)=1-Phi(0), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(0, Phi(0)=1-Phi(0), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0063/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 64. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":1}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(1, Phi(-1)=1-Phi(1), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(1, Phi(-1)=1-Phi(1), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0064/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 65. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":2}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(2, Phi(-2)=1-Phi(2), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(2, Phi(-2)=1-Phi(2), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0065/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 66. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":3}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(3, Phi(-3)=1-Phi(3), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(3, Phi(-3)=1-Phi(3), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0066/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 67. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":4}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(4, Phi(-4)=1-Phi(4), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(4, Phi(-4)=1-Phi(4), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0067/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 68. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":5}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(5, Phi(-5)=1-Phi(5), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(5, Phi(-5)=1-Phi(5), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0068/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 69. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":6}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(6, Phi(-6)=1-Phi(6), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(6, Phi(-6)=1-Phi(6), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0069/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 70. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":7}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(7, Phi(-7)=1-Phi(7), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(7, Phi(-7)=1-Phi(7), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0070/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 71. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":8}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(8, Phi(-8)=1-Phi(8), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(8, Phi(-8)=1-Phi(8), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0071/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 72. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":9}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(9, Phi(-9)=1-Phi(9), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(9, Phi(-9)=1-Phi(9), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0072/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 73. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":10}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(10, Phi(-10)=1-Phi(10), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(10, Phi(-10)=1-Phi(10), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0073/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 74. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":11}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(11, Phi(-11)=1-Phi(11), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(11, Phi(-11)=1-Phi(11), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0074/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 75. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-cdf-symmetry；資料={"x":12}。請依 [x, CDF_symmetry_identity, CDF_at_zero, declared_symmetry_certificate, boundary] 欄序回答。

查看答案與解釋(12, Phi(-12)=1-Phi(12), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)

Wave6第八層核對=(12, Phi(-12)=1-Phi(12), Phi(0)=1/2, 是, declared_normalization_plus_even_density_implies_CDF_symmetry_but_no_nonzero_elementary_CDF_value)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0075/)

標準常態分布 · qf-mod45-normaldist-cdf-symmetry · candidate





## 76. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":1,"panels":10}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(1, 10, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(1, 10, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0076/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 77. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":2,"panels":11}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(2, 11, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(2, 11, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0077/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 78. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":3,"panels":12}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(3, 12, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(3, 12, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0078/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 79. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":4,"panels":13}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(4, 13, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(4, 13, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0079/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 80. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":5,"panels":14}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(5, 14, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(5, 14, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0080/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 81. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":6,"panels":15}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(6, 15, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(6, 15, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0081/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 82. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":7,"panels":16}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(7, 16, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(7, 16, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0082/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 83. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":8,"panels":17}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(8, 17, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(8, 17, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0083/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 84. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":9,"panels":18}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(9, 18, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(9, 18, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0084/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 85. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":10,"panels":19}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(10, 19, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(10, 19, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0085/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 86. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":11,"panels":20}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(11, 20, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(11, 20, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0086/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 87. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":12,"panels":21}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(12, 21, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(12, 21, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0087/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 88. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":13,"panels":22}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(13, 22, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(13, 22, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0088/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 89. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":14,"panels":23}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(14, 23, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(14, 23, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0089/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 90. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":15,"panels":24}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(15, 24, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(15, 24, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0090/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 91. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":16,"panels":25}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(16, 25, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(16, 25, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0091/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 92. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":17,"panels":26}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(17, 26, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(17, 26, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0092/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 93. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":18,"panels":27}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(18, 27, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(18, 27, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0093/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 94. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":19,"panels":28}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(19, 28, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(19, 28, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0094/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 95. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":20,"panels":29}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(20, 29, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(20, 29, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0095/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 96. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":21,"panels":30}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(21, 30, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(21, 30, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0096/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 97. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":22,"panels":31}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(22, 31, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(22, 31, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0097/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 98. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":23,"panels":32}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(23, 32, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(23, 32, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0098/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 99. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":24,"panels":33}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(24, 33, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(24, 33, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0099/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate





## 100. 標準常態分布

standard normal的Gaussian density、evenness與declared normalization責任。操作=normaldist-normalization-moment-boundary；資料={"window":25,"panels":34}。請依 [window, panels, finite_method_scope, finite_method_proof_claim, normalization_named_fact, mean_named_fact, variance_named_fact, boundary] 欄序回答。

此題只記window/panels與有限方法範圍，未執行或提供Gaussian integral完整證明；named facts不由有限quadrature接受，也不被否旗標否定。

查看答案與解釋(25, 34, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)

Wave6第八層核對=(25, 34, finite_quadrature_only, 否, named_fact:integral_R_phi=1, named_fact:E[Z]=0, named_fact:Var(Z)=1, finite_window_or_panel_count_does_not_prove_normalization_or_moments)；依完整明示資料獨立重算；Phi(0)=1/2與Phi(-x)=1-Phi(x)只由已宣告normalization及symmetry推出；Gaussian integral、mean 0與variance 1是named theorem facts；finite quadrature不證它們或非零CDF exact value。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r04-standard-normal-distribution-0100/)

標準常態分布 · qf-mod45-normaldist-normalization-moment-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r04-standard-normal-distribution-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r04-standard-normal-distribution-foundations/validation-report.json)