# 估計量均方誤差基礎 · 脈衝 R05

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-r05-estimator-mean-squared-error-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. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-12,"support":[-13,-12,-11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-12, [[-13, 1/4, 1, 1/4], [-12, 1/2, 0, 0], [-11, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-12, [[-13, 1/4, 1, 1/4], [-12, 1/2, 0, 0], [-11, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0001/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 2. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-11,"support":[-13,-11,-9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-11, [[-13, 1/4, 4, 1], [-11, 1/2, 0, 0], [-9, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-11, [[-13, 1/4, 4, 1], [-11, 1/2, 0, 0], [-9, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0002/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 3. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-10,"support":[-13,-10,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-10, [[-13, 1/4, 9, 9/4], [-10, 1/2, 0, 0], [-7, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-10, [[-13, 1/4, 9, 9/4], [-10, 1/2, 0, 0], [-7, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0003/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 4. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-9,"support":[-13,-9,-5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-9, [[-13, 1/4, 16, 4], [-9, 1/2, 0, 0], [-5, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-9, [[-13, 1/4, 16, 4], [-9, 1/2, 0, 0], [-5, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0004/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 5. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-8,"support":[-13,-8,-3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-8, [[-13, 1/4, 25, 25/4], [-8, 1/2, 0, 0], [-3, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-8, [[-13, 1/4, 25, 25/4], [-8, 1/2, 0, 0], [-3, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0005/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 6. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-7,"support":[-8,-7,-6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-7, [[-8, 1/4, 1, 1/4], [-7, 1/2, 0, 0], [-6, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-7, [[-8, 1/4, 1, 1/4], [-7, 1/2, 0, 0], [-6, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0006/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 7. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-6,"support":[-8,-6,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-6, [[-8, 1/4, 4, 1], [-6, 1/2, 0, 0], [-4, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-6, [[-8, 1/4, 4, 1], [-6, 1/2, 0, 0], [-4, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0007/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 8. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-5,"support":[-8,-5,-2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-5, [[-8, 1/4, 9, 9/4], [-5, 1/2, 0, 0], [-2, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-5, [[-8, 1/4, 9, 9/4], [-5, 1/2, 0, 0], [-2, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0008/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 9. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-4,"support":[-8,-4,0],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-4, [[-8, 1/4, 16, 4], [-4, 1/2, 0, 0], [0, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-4, [[-8, 1/4, 16, 4], [-4, 1/2, 0, 0], [0, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0009/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 10. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-3,"support":[-8,-3,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(-3, [[-8, 1/4, 25, 25/4], [-3, 1/2, 0, 0], [2, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(-3, [[-8, 1/4, 25, 25/4], [-3, 1/2, 0, 0], [2, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0010/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 11. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-2,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

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

Wave6第八層核對=(-2, [[-3, 1/4, 1, 1/4], [-2, 1/2, 0, 0], [-1, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0011/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 12. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":-1,"support":[-3,-1,1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

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

Wave6第八層核對=(-1, [[-3, 1/4, 4, 1], [-1, 1/2, 0, 0], [1, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0012/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 13. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":0,"support":[-3,0,3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

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

Wave6第八層核對=(0, [[-3, 1/4, 9, 9/4], [0, 1/2, 0, 0], [3, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0013/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 14. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":1,"support":[-3,1,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(1, [[-3, 1/4, 16, 4], [1, 1/2, 0, 0], [5, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(1, [[-3, 1/4, 16, 4], [1, 1/2, 0, 0], [5, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0014/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 15. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":2,"support":[-3,2,7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(2, [[-3, 1/4, 25, 25/4], [2, 1/2, 0, 0], [7, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(2, [[-3, 1/4, 25, 25/4], [2, 1/2, 0, 0], [7, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0015/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 16. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":3,"support":[2,3,4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

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

Wave6第八層核對=(3, [[2, 1/4, 1, 1/4], [3, 1/2, 0, 0], [4, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0016/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 17. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":4,"support":[2,4,6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

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

Wave6第八層核對=(4, [[2, 1/4, 4, 1], [4, 1/2, 0, 0], [6, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0017/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 18. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":5,"support":[2,5,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(5, [[2, 1/4, 9, 9/4], [5, 1/2, 0, 0], [8, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(5, [[2, 1/4, 9, 9/4], [5, 1/2, 0, 0], [8, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0018/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 19. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":6,"support":[2,6,10],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(6, [[2, 1/4, 16, 4], [6, 1/2, 0, 0], [10, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(6, [[2, 1/4, 16, 4], [6, 1/2, 0, 0], [10, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0019/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 20. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":7,"support":[2,7,12],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(7, [[2, 1/4, 25, 25/4], [7, 1/2, 0, 0], [12, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(7, [[2, 1/4, 25, 25/4], [7, 1/2, 0, 0], [12, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0020/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 21. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":8,"support":[7,8,9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(8, [[7, 1/4, 1, 1/4], [8, 1/2, 0, 0], [9, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(8, [[7, 1/4, 1, 1/4], [8, 1/2, 0, 0], [9, 1/4, 1, 1/4]], 1/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0021/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 22. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":9,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(9, [[7, 1/4, 4, 1], [9, 1/2, 0, 0], [11, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(9, [[7, 1/4, 4, 1], [9, 1/2, 0, 0], [11, 1/4, 4, 1]], 2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0022/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 23. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":10,"support":[7,10,13],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(10, [[7, 1/4, 9, 9/4], [10, 1/2, 0, 0], [13, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(10, [[7, 1/4, 9, 9/4], [10, 1/2, 0, 0], [13, 1/4, 9, 9/4]], 9/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0023/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 24. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":11,"support":[7,11,15],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(11, [[7, 1/4, 16, 4], [11, 1/2, 0, 0], [15, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(11, [[7, 1/4, 16, 4], [11, 1/2, 0, 0], [15, 1/4, 16, 4]], 8, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0024/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 25. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-single-theta-exact；資料={"theta":12,"support":[7,12,17],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, weighted_error_rows, MSE, certificate] 欄序回答。

查看答案與解釋(12, [[7, 1/4, 25, 25/4], [12, 1/2, 0, 0], [17, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)

Wave6第八層核對=(12, [[7, 1/4, 25, 25/4], [12, 1/2, 0, 0], [17, 1/4, 25, 25/4]], 25/2, direct_expected_squared_error_without_bias_variance_decomposition)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0025/)

估計量均方誤差 · qf-mod45-mse-single-theta-exact · candidate





## 26. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-12,[-13,-12,-11],[[1,4],[1,2],[1,4]]],[-11,[-12,-11,-10],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-11, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], 1/2], [-12, [[-13, 1/4], [-12, 1/2], [-11, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-11, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], 1/2], [-12, [[-13, 1/4], [-12, 1/2], [-11, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0026/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 27. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-11,[-13,-11,-9],[[1,4],[1,2],[1,4]]],[-10,[-11,-10,-9],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-10, [[-11, 1/4], [-10, 1/2], [-9, 1/4]], 1/2], [-11, [[-13, 1/4], [-11, 1/2], [-9, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-10, [[-11, 1/4], [-10, 1/2], [-9, 1/4]], 1/2], [-11, [[-13, 1/4], [-11, 1/2], [-9, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0027/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 28. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-10,[-13,-10,-7],[[1,4],[1,2],[1,4]]],[-9,[-10,-9,-8],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-10, [[-13, 1/4], [-10, 1/2], [-7, 1/4]], 9/2], [-9, [[-10, 1/4], [-9, 1/2], [-8, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-10, [[-13, 1/4], [-10, 1/2], [-7, 1/4]], 9/2], [-9, [[-10, 1/4], [-9, 1/2], [-8, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0028/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 29. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-9,[-13,-9,-5],[[1,4],[1,2],[1,4]]],[-8,[-9,-8,-7],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-8, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], 1/2], [-9, [[-13, 1/4], [-9, 1/2], [-5, 1/4]], 8]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-8, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], 1/2], [-9, [[-13, 1/4], [-9, 1/2], [-5, 1/4]], 8]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0029/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 30. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-8,[-13,-8,-3],[[1,4],[1,2],[1,4]]],[-7,[-8,-7,-6],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-7, [[-8, 1/4], [-7, 1/2], [-6, 1/4]], 1/2], [-8, [[-13, 1/4], [-8, 1/2], [-3, 1/4]], 25/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-7, [[-8, 1/4], [-7, 1/2], [-6, 1/4]], 1/2], [-8, [[-13, 1/4], [-8, 1/2], [-3, 1/4]], 25/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0030/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 31. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-7,[-8,-7,-6],[[1,4],[1,2],[1,4]]],[-6,[-7,-6,-5],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-6, [[-7, 1/4], [-6, 1/2], [-5, 1/4]], 1/2], [-7, [[-8, 1/4], [-7, 1/2], [-6, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-6, [[-7, 1/4], [-6, 1/2], [-5, 1/4]], 1/2], [-7, [[-8, 1/4], [-7, 1/2], [-6, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0031/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 32. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-6,[-8,-6,-4],[[1,4],[1,2],[1,4]]],[-5,[-6,-5,-4],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-5, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], 1/2], [-6, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-5, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], 1/2], [-6, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0032/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 33. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-5,[-8,-5,-2],[[1,4],[1,2],[1,4]]],[-4,[-5,-4,-3],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-4, [[-5, 1/4], [-4, 1/2], [-3, 1/4]], 1/2], [-5, [[-8, 1/4], [-5, 1/2], [-2, 1/4]], 9/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-4, [[-5, 1/4], [-4, 1/2], [-3, 1/4]], 1/2], [-5, [[-8, 1/4], [-5, 1/2], [-2, 1/4]], 9/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0033/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 34. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-4,[-8,-4,0],[[1,4],[1,2],[1,4]]],[-3,[-4,-3,-2],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-3, [[-4, 1/4], [-3, 1/2], [-2, 1/4]], 1/2], [-4, [[-8, 1/4], [-4, 1/2], [0, 1/4]], 8]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-3, [[-4, 1/4], [-3, 1/2], [-2, 1/4]], 1/2], [-4, [[-8, 1/4], [-4, 1/2], [0, 1/4]], 8]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0034/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 35. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-3,[-8,-3,2],[[1,4],[1,2],[1,4]]],[-2,[-3,-2,-1],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[-2, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], 1/2], [-3, [[-8, 1/4], [-3, 1/2], [2, 1/4]], 25/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[-2, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], 1/2], [-3, [[-8, 1/4], [-3, 1/2], [2, 1/4]], 25/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0035/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 36. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-2,[-3,-2,-1],[[1,4],[1,2],[1,4]]],[-1,[-2,-1,0],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

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

Wave6第八層核對=([[-1, [[-2, 1/4], [-1, 1/2], [0, 1/4]], 1/2], [-2, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0036/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 37. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[-1,[-3,-1,1],[[1,4],[1,2],[1,4]]],[0,[-1,0,1],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

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

Wave6第八層核對=([[-1, [[-3, 1/4], [-1, 1/2], [1, 1/4]], 2], [0, [[-1, 1/4], [0, 1/2], [1, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0037/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 38. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[0,[-3,0,3],[[1,4],[1,2],[1,4]]],[1,[0,1,2],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

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

Wave6第八層核對=([[0, [[-3, 1/4], [0, 1/2], [3, 1/4]], 9/2], [1, [[0, 1/4], [1, 1/2], [2, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0038/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 39. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[1,[-3,1,5],[[1,4],[1,2],[1,4]]],[2,[1,2,3],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[1, [[-3, 1/4], [1, 1/2], [5, 1/4]], 8], [2, [[1, 1/4], [2, 1/2], [3, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[1, [[-3, 1/4], [1, 1/2], [5, 1/4]], 8], [2, [[1, 1/4], [2, 1/2], [3, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0039/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 40. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[2,[-3,2,7],[[1,4],[1,2],[1,4]]],[3,[2,3,4],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[2, [[-3, 1/4], [2, 1/2], [7, 1/4]], 25/2], [3, [[2, 1/4], [3, 1/2], [4, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[2, [[-3, 1/4], [2, 1/2], [7, 1/4]], 25/2], [3, [[2, 1/4], [3, 1/2], [4, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0040/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 41. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[3,[2,3,4],[[1,4],[1,2],[1,4]]],[4,[3,4,5],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

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

Wave6第八層核對=([[3, [[2, 1/4], [3, 1/2], [4, 1/4]], 1/2], [4, [[3, 1/4], [4, 1/2], [5, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0041/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 42. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[4,[2,4,6],[[1,4],[1,2],[1,4]]],[5,[4,5,6],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

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

Wave6第八層核對=([[4, [[2, 1/4], [4, 1/2], [6, 1/4]], 2], [5, [[4, 1/4], [5, 1/2], [6, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0042/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 43. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[5,[2,5,8],[[1,4],[1,2],[1,4]]],[6,[5,6,7],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[5, [[2, 1/4], [5, 1/2], [8, 1/4]], 9/2], [6, [[5, 1/4], [6, 1/2], [7, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[5, [[2, 1/4], [5, 1/2], [8, 1/4]], 9/2], [6, [[5, 1/4], [6, 1/2], [7, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0043/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 44. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[6,[2,6,10],[[1,4],[1,2],[1,4]]],[7,[6,7,8],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[6, [[2, 1/4], [6, 1/2], [10, 1/4]], 8], [7, [[6, 1/4], [7, 1/2], [8, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[6, [[2, 1/4], [6, 1/2], [10, 1/4]], 8], [7, [[6, 1/4], [7, 1/2], [8, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0044/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 45. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[7,[2,7,12],[[1,4],[1,2],[1,4]]],[8,[7,8,9],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[7, [[2, 1/4], [7, 1/2], [12, 1/4]], 25/2], [8, [[7, 1/4], [8, 1/2], [9, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[7, [[2, 1/4], [7, 1/2], [12, 1/4]], 25/2], [8, [[7, 1/4], [8, 1/2], [9, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0045/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 46. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[8,[7,8,9],[[1,4],[1,2],[1,4]]],[9,[8,9,10],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[8, [[7, 1/4], [8, 1/2], [9, 1/4]], 1/2], [9, [[8, 1/4], [9, 1/2], [10, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[8, [[7, 1/4], [8, 1/2], [9, 1/4]], 1/2], [9, [[8, 1/4], [9, 1/2], [10, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0046/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 47. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[9,[7,9,11],[[1,4],[1,2],[1,4]]],[10,[9,10,11],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[10, [[9, 1/4], [10, 1/2], [11, 1/4]], 1/2], [9, [[7, 1/4], [9, 1/2], [11, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[10, [[9, 1/4], [10, 1/2], [11, 1/4]], 1/2], [9, [[7, 1/4], [9, 1/2], [11, 1/4]], 2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0047/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 48. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[10,[7,10,13],[[1,4],[1,2],[1,4]]],[11,[10,11,12],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[10, [[7, 1/4], [10, 1/2], [13, 1/4]], 9/2], [11, [[10, 1/4], [11, 1/2], [12, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[10, [[7, 1/4], [10, 1/2], [13, 1/4]], 9/2], [11, [[10, 1/4], [11, 1/2], [12, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0048/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 49. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[11,[7,11,15],[[1,4],[1,2],[1,4]]],[12,[11,12,13],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[11, [[7, 1/4], [11, 1/2], [15, 1/4]], 8], [12, [[11, 1/4], [12, 1/2], [13, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[11, [[7, 1/4], [11, 1/2], [15, 1/4]], 8], [12, [[11, 1/4], [12, 1/2], [13, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0049/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 50. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-multi-theta-table；資料={"laws":[[12,[7,12,17],[[1,4],[1,2],[1,4]]],[13,[12,13,14],[[1,4],[1,2],[1,4]]]]}。請依 [law_risk_rows, certificate] 欄序回答。

查看答案與解釋([[12, [[7, 1/4], [12, 1/2], [17, 1/4]], 25/2], [13, [[12, 1/4], [13, 1/2], [14, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)

Wave6第八層核對=([[12, [[7, 1/4], [12, 1/2], [17, 1/4]], 25/2], [13, [[12, 1/4], [13, 1/2], [14, 1/4]], 1/2]], MSE_is_computed_separately_under_each_complete_P_theta_law)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0050/)

估計量均方誤差 · qf-mod45-mse-multi-theta-table · candidate





## 51. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-12,"support":[-12,-11],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-12, [[-12, 1, 0, 0], [-11, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-12, [[-12, 1, 0, 0], [-11, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0051/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 52. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-11,"support":[-11,-9],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-11, [[-11, 1, 0, 0], [-9, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-11, [[-11, 1, 0, 0], [-9, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0052/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 53. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-10,"support":[-10,-7],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-10, [[-10, 1, 0, 0], [-7, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-10, [[-10, 1, 0, 0], [-7, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0053/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 54. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-9,"support":[-9,-5],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-9, [[-9, 1, 0, 0], [-5, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-9, [[-9, 1, 0, 0], [-5, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0054/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 55. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-8,"support":[-8,-3],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-8, [[-8, 1, 0, 0], [-3, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-8, [[-8, 1, 0, 0], [-3, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0055/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 56. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-7,"support":[-7,-6],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-7, [[-7, 1, 0, 0], [-6, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-7, [[-7, 1, 0, 0], [-6, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0056/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 57. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-6,"support":[-6,-4],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

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

Wave6第八層核對=(-6, [[-6, 1, 0, 0], [-4, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0057/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 58. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-5,"support":[-5,-2],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-5, [[-5, 1, 0, 0], [-2, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-5, [[-5, 1, 0, 0], [-2, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0058/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 59. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-4,"support":[-4,0],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-4, [[-4, 1, 0, 0], [0, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-4, [[-4, 1, 0, 0], [0, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0059/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 60. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-3,"support":[-3,2],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-3, [[-3, 1, 0, 0], [2, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-3, [[-3, 1, 0, 0], [2, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0060/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 61. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-2,"support":[-2,-1],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

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

Wave6第八層核對=(-2, [[-2, 1, 0, 0], [-1, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0061/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 62. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":-1,"support":[-1,1],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(-1, [[-1, 1, 0, 0], [1, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(-1, [[-1, 1, 0, 0], [1, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0062/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 63. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":0,"support":[0,3],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(0, [[0, 1, 0, 0], [3, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(0, [[0, 1, 0, 0], [3, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0063/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 64. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":1,"support":[1,5],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(1, [[1, 1, 0, 0], [5, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(1, [[1, 1, 0, 0], [5, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0064/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 65. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":2,"support":[2,7],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(2, [[2, 1, 0, 0], [7, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(2, [[2, 1, 0, 0], [7, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0065/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 66. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":3,"support":[3,4],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

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

Wave6第八層核對=(3, [[3, 1, 0, 0], [4, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0066/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 67. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":4,"support":[4,6],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(4, [[4, 1, 0, 0], [6, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(4, [[4, 1, 0, 0], [6, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0067/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 68. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":5,"support":[5,8],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(5, [[5, 1, 0, 0], [8, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(5, [[5, 1, 0, 0], [8, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0068/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 69. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":6,"support":[6,10],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(6, [[6, 1, 0, 0], [10, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(6, [[6, 1, 0, 0], [10, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0069/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 70. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":7,"support":[7,12],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(7, [[7, 1, 0, 0], [12, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(7, [[7, 1, 0, 0], [12, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0070/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 71. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":8,"support":[8,9],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(8, [[8, 1, 0, 0], [9, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(8, [[8, 1, 0, 0], [9, 0, 1, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0071/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 72. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":9,"support":[9,11],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(9, [[9, 1, 0, 0], [11, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(9, [[9, 1, 0, 0], [11, 0, 4, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0072/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 73. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":10,"support":[10,13],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(10, [[10, 1, 0, 0], [13, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(10, [[10, 1, 0, 0], [13, 0, 9, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0073/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 74. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":11,"support":[11,15],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(11, [[11, 1, 0, 0], [15, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(11, [[11, 1, 0, 0], [15, 0, 16, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0074/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 75. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-zero-iff-almost-sure；資料={"theta":12,"support":[12,17],"probabilities":[1,0]}。請依 [theta, weighted_error_rows, MSE, zero_MSE, almost_surely_equal_theta, equivalence_holds, certificate] 欄序回答。

almost surely只約束正機率值；零質量列仍保留，不必等於theta。equivalence_holds不等於zero_MSE旗標本身。

查看答案與解釋(12, [[12, 1, 0, 0], [17, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)

Wave6第八層核對=(12, [[12, 1, 0, 0], [17, 0, 25, 0]], 0, 是, 是, 是, nonnegative_squared_terms_make_zero_MSE_equivalent_to_T_equals_theta_almost_surely)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0075/)

估計量均方誤差 · qf-mod45-mse-zero-iff-almost-sure · candidate





## 76. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-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, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(-12, -13, 1, -12, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0076/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 77. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-11,"support":[-13,-11,-9],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-11, -13, 4, -11, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-11, -13, 4, -11, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0077/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 78. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-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, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(-10, -13, 9, -10, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0078/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 79. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-9,"support":[-13,-9,-5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-9, -13, 16, -9, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-9, -13, 16, -9, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0079/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 80. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-8,"support":[-13,-8,-3],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-8, -13, 25, -8, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-8, -13, 25, -8, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0080/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 81. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-7,"support":[-8,-7,-6],"probabilities":[[1,4],[1,2],[1,4]],"observed":-8}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-7, -8, 1, -7, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-7, -8, 1, -7, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0081/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 82. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-6,"support":[-8,-6,-4],"probabilities":[[1,4],[1,2],[1,4]],"observed":-8}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-6, -8, 4, -6, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-6, -8, 4, -6, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0082/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 83. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-5,"support":[-8,-5,-2],"probabilities":[[1,4],[1,2],[1,4]],"observed":-8}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(-5, -8, 9, -5, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0083/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 84. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-4,"support":[-8,-4,0],"probabilities":[[1,4],[1,2],[1,4]],"observed":-8}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-4, -8, 16, -4, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-4, -8, 16, -4, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0084/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 85. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-3,"support":[-8,-3,2],"probabilities":[[1,4],[1,2],[1,4]],"observed":-8}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-3, -8, 25, -3, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-3, -8, 25, -3, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0085/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 86. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-2,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(-2, -3, 1, -2, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0086/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 87. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":-1,"support":[-3,-1,1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(-1, -3, 4, -1, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(-1, -3, 4, -1, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0087/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 88. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":0,"support":[-3,0,3],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(0, -3, 9, 0, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0088/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 89. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":1,"support":[-3,1,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(1, -3, 16, 1, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(1, -3, 16, 1, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0089/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 90. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":2,"support":[-3,2,7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(2, -3, 25, 2, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(2, -3, 25, 2, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0090/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 91. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":3,"support":[2,3,4],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(3, 2, 1, 3, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0091/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 92. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-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, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

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

Wave6第八層核對=(4, 2, 4, 4, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0092/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 93. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":5,"support":[2,5,8],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(5, 2, 9, 5, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(5, 2, 9, 5, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0093/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 94. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":6,"support":[2,6,10],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(6, 2, 16, 6, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(6, 2, 16, 6, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0094/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 95. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":7,"support":[2,7,12],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(7, 2, 25, 7, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(7, 2, 25, 7, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0095/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 96. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":8,"support":[7,8,9],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(8, 7, 1, 8, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(8, 7, 1, 8, 是, 1/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0096/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 97. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":9,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(9, 7, 4, 9, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(9, 7, 4, 9, 是, 2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0097/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 98. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":10,"support":[7,10,13],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(10, 7, 9, 10, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(10, 7, 9, 10, 是, 9/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0098/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 99. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":11,"support":[7,11,15],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(11, 7, 16, 11, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(11, 7, 16, 11, 是, 8, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0099/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate





## 100. 估計量均方誤差

scalar theta下完整finite sampling law的exact expected squared error。操作=mse-observed-unbiased-boundary；資料={"theta":12,"support":[7,12,17],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, mean, unbiased, MSE, observed_error_equals_MSE, unbiased_with_positive_MSE, observed_or_unbiased_consistency_claim, boundary] 欄序回答。

observed_error_equals_MSE可碰巧為是；最後的否不否定此數值相等，也不把unbiased推成zero MSE或consistency。

查看答案與解釋(12, 7, 25, 12, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)

Wave6第八層核對=(12, 7, 25, 12, 是, 25/2, 否, 是, 否, one_observed_squared_error_is_not_MSE_and_unbiased_does_not_imply_zero_MSE_or_consistency)；依完整明示資料獨立重算；MSE逐theta直接加權平方誤差；MSE=0恰當T=theta almost surely；單一observed error不是MSE；unbiased不推出zero MSE，亦不使用bias-variance decomposition或推出consistency。



[本題逐步詳解（AI 二次覆核）](https://ocme.evemisslab.com/zh-Hant/questions/q-20261015-advance-20261114-r05-estimator-mean-squared-error-0100/)

估計量均方誤差 · qf-mod45-mse-observed-unbiased-boundary · candidate



[原始題目 JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r05-estimator-mean-squared-error-foundations/questions.jsonl) · [驗收報告](https://ocme.evemisslab.com/data/questions/batches/batch-20261015-advance-20261114-r05-estimator-mean-squared-error-foundations/validation-report.json)