# 偏誤－變異數分解基礎 · 脈衝 R03

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-20261115-r03-bias-variance-decomposition-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. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-12,"support":[-12,-11,-10],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-12, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], -11, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-12, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], -11, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0001/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 2. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-11,"support":[-11,-9,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-11, [[-11, 1/4], [-9, 1/2], [-7, 1/4]], -9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-11, [[-11, 1/4], [-9, 1/2], [-7, 1/4]], -9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0002/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 3. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-10,"support":[-10,-7,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-10, [[-10, 1/4], [-7, 1/2], [-4, 1/4]], -7, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-10, [[-10, 1/4], [-7, 1/2], [-4, 1/4]], -7, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0003/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 4. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-9,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-9, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], -8, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-9, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], -8, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0004/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 5. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-8,"support":[-8,-6,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-8, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], -6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-8, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], -6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0005/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 6. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-7,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-7, [[-7, 1/4], [-4, 1/2], [-1, 1/4]], -4, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-7, [[-7, 1/4], [-4, 1/2], [-1, 1/4]], -4, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0006/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 7. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-6,"support":[-6,-5,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-6, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], -5, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-6, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], -5, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0007/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 8. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-5,"support":[-5,-3,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-5, [[-5, 1/4], [-3, 1/2], [-1, 1/4]], -3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-5, [[-5, 1/4], [-3, 1/2], [-1, 1/4]], -3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0008/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 9. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-4,"support":[-4,-1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-4, [[-4, 1/4], [-1, 1/2], [2, 1/4]], -1, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-4, [[-4, 1/4], [-1, 1/2], [2, 1/4]], -1, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0009/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 10. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-3,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-3, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], -2, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-3, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], -2, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0010/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 11. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-2,"support":[-2,0,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-2, [[-2, 1/4], [0, 1/2], [2, 1/4]], 0, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-2, [[-2, 1/4], [0, 1/2], [2, 1/4]], 0, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0011/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 12. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-1,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(-1, [[-1, 1/4], [2, 1/2], [5, 1/4]], 2, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(-1, [[-1, 1/4], [2, 1/2], [5, 1/4]], 2, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0012/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 13. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":0,"support":[0,1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

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

Wave6第九層核對=(0, [[0, 1/4], [1, 1/2], [2, 1/4]], 1, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0013/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 14. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":1,"support":[1,3,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

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

Wave6第九層核對=(1, [[1, 1/4], [3, 1/2], [5, 1/4]], 3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0014/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 15. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":2,"support":[2,5,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(2, [[2, 1/4], [5, 1/2], [8, 1/4]], 5, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(2, [[2, 1/4], [5, 1/2], [8, 1/4]], 5, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0015/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 16. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":3,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

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

Wave6第九層核對=(3, [[3, 1/4], [4, 1/2], [5, 1/4]], 4, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0016/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 17. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":4,"support":[4,6,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(4, [[4, 1/4], [6, 1/2], [8, 1/4]], 6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(4, [[4, 1/4], [6, 1/2], [8, 1/4]], 6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0017/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 18. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":5,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(5, [[5, 1/4], [8, 1/2], [11, 1/4]], 8, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(5, [[5, 1/4], [8, 1/2], [11, 1/4]], 8, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0018/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 19. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":6,"support":[6,7,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(6, [[6, 1/4], [7, 1/2], [8, 1/4]], 7, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(6, [[6, 1/4], [7, 1/2], [8, 1/4]], 7, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0019/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 20. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":7,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(7, [[7, 1/4], [9, 1/2], [11, 1/4]], 9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(7, [[7, 1/4], [9, 1/2], [11, 1/4]], 9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0020/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 21. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":8,"support":[8,11,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(8, [[8, 1/4], [11, 1/2], [14, 1/4]], 11, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(8, [[8, 1/4], [11, 1/2], [14, 1/4]], 11, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0021/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 22. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":9,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(9, [[9, 1/4], [10, 1/2], [11, 1/4]], 10, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(9, [[9, 1/4], [10, 1/2], [11, 1/4]], 10, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0022/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 23. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":10,"support":[10,12,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(10, [[10, 1/4], [12, 1/2], [14, 1/4]], 12, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(10, [[10, 1/4], [12, 1/2], [14, 1/4]], 12, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0023/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 24. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":11,"support":[11,14,17],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(11, [[11, 1/4], [14, 1/2], [17, 1/4]], 14, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(11, [[11, 1/4], [14, 1/2], [17, 1/4]], 14, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0024/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 25. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":12,"support":[12,13,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。

查看答案與解釋(12, [[12, 1/4], [13, 1/2], [14, 1/4]], 13, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)

Wave6第九層核對=(12, [[12, 1/4], [13, 1/2], [14, 1/4]], 13, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0025/)

偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate





## 26. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-12,"support":[-11,-10,-9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0026/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 27. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-11,"support":[-10,-9,-8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0027/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 28. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-10,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0028/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 29. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-9,"support":[-8,-7,-6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0029/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 30. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-8,"support":[-7,-6,-5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0030/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 31. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-7,"support":[-6,-5,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0031/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 32. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-6,"support":[-5,-4,-3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0032/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 33. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-5,"support":[-4,-3,-2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0033/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 34. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-4,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0034/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 35. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-3,"support":[-2,-1,0],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(-1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(-1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0035/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 36. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-2,"support":[-1,0,1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(0, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(0, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0036/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 37. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-1,"support":[0,1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0037/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 38. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":0,"support":[1,2,3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0038/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 39. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":1,"support":[2,3,4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0039/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 40. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":2,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0040/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 41. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":3,"support":[4,5,6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0041/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 42. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":4,"support":[5,6,7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0042/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 43. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":5,"support":[6,7,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0043/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 44. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":6,"support":[7,8,9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0044/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 45. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":7,"support":[8,9,10],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0045/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 46. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":8,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0046/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 47. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":9,"support":[10,11,12],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(11, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(11, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0047/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 48. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":10,"support":[11,12,13],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(12, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(12, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0048/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 49. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":11,"support":[12,13,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(13, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(13, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0049/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 50. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":12,"support":[13,14,15],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。

查看答案與解釋(14, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)

Wave6第九層核對=(14, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0050/)

偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate





## 51. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-12,[-12,-11,-10],[[1,4],[1,2],[1,4]]],[-11,[-12,-11,-10],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-11, -11, 0, 1/2, 1/2, 1/2, 是], [-12, -11, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-11, -11, 0, 1/2, 1/2, 1/2, 是], [-12, -11, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0051/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 52. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-11,[-11,-9,-7],[[1,4],[1,2],[1,4]]],[-10,[-11,-10,-9],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-10, -10, 0, 1/2, 1/2, 1/2, 是], [-11, -9, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-10, -10, 0, 1/2, 1/2, 1/2, 是], [-11, -9, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0052/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 53. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-10,[-10,-7,-4],[[1,4],[1,2],[1,4]]],[-9,[-10,-9,-8],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-10, -7, 3, 9/2, 27/2, 27/2, 是], [-9, -9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-10, -7, 3, 9/2, 27/2, 27/2, 是], [-9, -9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0053/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 54. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-9,[-9,-8,-7],[[1,4],[1,2],[1,4]]],[-8,[-9,-8,-7],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-8, -8, 0, 1/2, 1/2, 1/2, 是], [-9, -8, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-8, -8, 0, 1/2, 1/2, 1/2, 是], [-9, -8, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0054/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 55. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-8,[-8,-6,-4],[[1,4],[1,2],[1,4]]],[-7,[-8,-7,-6],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-7, -7, 0, 1/2, 1/2, 1/2, 是], [-8, -6, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-7, -7, 0, 1/2, 1/2, 1/2, 是], [-8, -6, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0055/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 56. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-7,[-7,-4,-1],[[1,4],[1,2],[1,4]]],[-6,[-7,-6,-5],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-6, -6, 0, 1/2, 1/2, 1/2, 是], [-7, -4, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-6, -6, 0, 1/2, 1/2, 1/2, 是], [-7, -4, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0056/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 57. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-6,[-6,-5,-4],[[1,4],[1,2],[1,4]]],[-5,[-6,-5,-4],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-5, -5, 0, 1/2, 1/2, 1/2, 是], [-6, -5, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-5, -5, 0, 1/2, 1/2, 1/2, 是], [-6, -5, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0057/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 58. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-5,[-5,-3,-1],[[1,4],[1,2],[1,4]]],[-4,[-5,-4,-3],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-4, -4, 0, 1/2, 1/2, 1/2, 是], [-5, -3, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-4, -4, 0, 1/2, 1/2, 1/2, 是], [-5, -3, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0058/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 59. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-4,[-4,-1,2],[[1,4],[1,2],[1,4]]],[-3,[-4,-3,-2],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-3, -3, 0, 1/2, 1/2, 1/2, 是], [-4, -1, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-3, -3, 0, 1/2, 1/2, 1/2, 是], [-4, -1, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0059/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 60. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-3,[-3,-2,-1],[[1,4],[1,2],[1,4]]],[-2,[-3,-2,-1],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-2, -2, 0, 1/2, 1/2, 1/2, 是], [-3, -2, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-2, -2, 0, 1/2, 1/2, 1/2, 是], [-3, -2, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0060/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 61. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-2,[-2,0,2],[[1,4],[1,2],[1,4]]],[-1,[-2,-1,0],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-1, -1, 0, 1/2, 1/2, 1/2, 是], [-2, 0, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-1, -1, 0, 1/2, 1/2, 1/2, 是], [-2, 0, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0061/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 62. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-1,[-1,2,5],[[1,4],[1,2],[1,4]]],[0,[-1,0,1],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[-1, 2, 3, 9/2, 27/2, 27/2, 是], [0, 0, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[-1, 2, 3, 9/2, 27/2, 27/2, 是], [0, 0, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0062/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 63. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[0,[0,1,2],[[1,4],[1,2],[1,4]]],[1,[0,1,2],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[0, 1, 1, 1/2, 3/2, 3/2, 是], [1, 1, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[0, 1, 1, 1/2, 3/2, 3/2, 是], [1, 1, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0063/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 64. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[1,[1,3,5],[[1,4],[1,2],[1,4]]],[2,[1,2,3],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[1, 3, 2, 2, 6, 6, 是], [2, 2, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[1, 3, 2, 2, 6, 6, 是], [2, 2, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0064/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 65. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[2,[2,5,8],[[1,4],[1,2],[1,4]]],[3,[2,3,4],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[2, 5, 3, 9/2, 27/2, 27/2, 是], [3, 3, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[2, 5, 3, 9/2, 27/2, 27/2, 是], [3, 3, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0065/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 66. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[3,[3,4,5],[[1,4],[1,2],[1,4]]],[4,[3,4,5],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

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

Wave6第九層核對=([[3, 4, 1, 1/2, 3/2, 3/2, 是], [4, 4, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0066/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 67. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[4,[4,6,8],[[1,4],[1,2],[1,4]]],[5,[4,5,6],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[4, 6, 2, 2, 6, 6, 是], [5, 5, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[4, 6, 2, 2, 6, 6, 是], [5, 5, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0067/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 68. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[5,[5,8,11],[[1,4],[1,2],[1,4]]],[6,[5,6,7],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[5, 8, 3, 9/2, 27/2, 27/2, 是], [6, 6, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[5, 8, 3, 9/2, 27/2, 27/2, 是], [6, 6, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0068/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 69. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[6,[6,7,8],[[1,4],[1,2],[1,4]]],[7,[6,7,8],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[6, 7, 1, 1/2, 3/2, 3/2, 是], [7, 7, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[6, 7, 1, 1/2, 3/2, 3/2, 是], [7, 7, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0069/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 70. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[7,[7,9,11],[[1,4],[1,2],[1,4]]],[8,[7,8,9],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[7, 9, 2, 2, 6, 6, 是], [8, 8, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[7, 9, 2, 2, 6, 6, 是], [8, 8, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0070/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 71. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[8,[8,11,14],[[1,4],[1,2],[1,4]]],[9,[8,9,10],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[8, 11, 3, 9/2, 27/2, 27/2, 是], [9, 9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[8, 11, 3, 9/2, 27/2, 27/2, 是], [9, 9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0071/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 72. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[9,[9,10,11],[[1,4],[1,2],[1,4]]],[10,[9,10,11],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[10, 10, 0, 1/2, 1/2, 1/2, 是], [9, 10, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[10, 10, 0, 1/2, 1/2, 1/2, 是], [9, 10, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0072/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 73. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[10,[10,12,14],[[1,4],[1,2],[1,4]]],[11,[10,11,12],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[10, 12, 2, 2, 6, 6, 是], [11, 11, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[10, 12, 2, 2, 6, 6, 是], [11, 11, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0073/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 74. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[11,[11,14,17],[[1,4],[1,2],[1,4]]],[12,[11,12,13],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[11, 14, 3, 9/2, 27/2, 27/2, 是], [12, 12, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[11, 14, 3, 9/2, 27/2, 27/2, 是], [12, 12, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0074/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 75. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[12,[12,13,14],[[1,4],[1,2],[1,4]]],[13,[12,13,14],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。

查看答案與解釋([[12, 13, 1, 1/2, 3/2, 3/2, 是], [13, 13, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)

Wave6第九層核對=([[12, 13, 1, 1/2, 3/2, 3/2, 是], [13, 13, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0075/)

偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate





## 76. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-12,"support":[-13,-12,-11],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-12, -13, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-12, -13, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0076/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 77. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-11,"support":[-11,-9,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-11, -11, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-11, -11, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0077/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 78. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-10,"support":[-13,-10,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-10, -13, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-10, -13, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0078/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 79. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-9,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-9}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-9, -9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-9, -9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0079/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 80. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-8,"support":[-10,-8,-6],"probabilities":[[1,4],[1,2],[1,4]],"observed":-10}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-8, -10, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-8, -10, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0080/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 81. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-7,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-7, -7, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-7, -7, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0081/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 82. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-6,"support":[-7,-6,-5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-6, -7, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-6, -7, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0082/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 83. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-5,"support":[-5,-3,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-5, -5, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-5, -5, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0083/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 84. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-4,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-4, -7, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-4, -7, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0084/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 85. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-3,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-3, -3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-3, -3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0085/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 86. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-2,"support":[-4,-2,0],"probabilities":[[1,4],[1,2],[1,4]],"observed":-4}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-2, -4, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-2, -4, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0086/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 87. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-1,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(-1, -1, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(-1, -1, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0087/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 88. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":0,"support":[-1,0,1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(0, -1, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(0, -1, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0088/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 89. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":1,"support":[1,3,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(1, 1, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(1, 1, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0089/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 90. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":2,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(2, -1, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(2, -1, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0090/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 91. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":3,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":3}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(3, 3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(3, 3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0091/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 92. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":4,"support":[2,4,6],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(4, 2, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(4, 2, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0092/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 93. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":5,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(5, 5, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(5, 5, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0093/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 94. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":6,"support":[5,6,7],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(6, 5, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(6, 5, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0094/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 95. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":7,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(7, 7, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(7, 7, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0095/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 96. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":8,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(8, 5, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(8, 5, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0096/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 97. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":9,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":9}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(9, 9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(9, 9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0097/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 98. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":10,"support":[8,10,12],"probabilities":[[1,4],[1,2],[1,4]],"observed":8}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(10, 8, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(10, 8, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0098/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 99. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":11,"support":[11,14,17],"probabilities":[[1,4],[1,2],[1,4]],"observed":11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(11, 11, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(11, 11, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0099/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate





## 100. 偏誤－變異數分解

逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":12,"support":[11,12,13],"probabilities":[[1,4],[1,2],[1,4]],"observed":11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。

variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。

查看答案與解釋(12, 11, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)

Wave6第九層核對=(12, 11, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261115-r03-bias-variance-decomposition-0100/)

偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r03-bias-variance-decomposition-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261115-r03-bias-variance-decomposition-foundations/validation-report.json)