偏誤－變異數分解基礎 · 脈衝 R03
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261115-r03-bias-variance-decomposition-foundations · 2026-10-15 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
欄序與來源綁定資料
1. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-12,"support":[-12,-11,-10],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-12, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], -11, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-12, [[-12, 1/4], [-11, 1/2], [-10, 1/4]], -11, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
2. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-11,"support":[-11,-9,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-11, [[-11, 1/4], [-9, 1/2], [-7, 1/4]], -9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-11, [[-11, 1/4], [-9, 1/2], [-7, 1/4]], -9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
3. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-10,"support":[-10,-7,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-10, [[-10, 1/4], [-7, 1/2], [-4, 1/4]], -7, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-10, [[-10, 1/4], [-7, 1/2], [-4, 1/4]], -7, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
4. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-9,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-9, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], -8, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-9, [[-9, 1/4], [-8, 1/2], [-7, 1/4]], -8, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
5. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-8,"support":[-8,-6,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-8, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], -6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-8, [[-8, 1/4], [-6, 1/2], [-4, 1/4]], -6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
6. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-7,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-7, [[-7, 1/4], [-4, 1/2], [-1, 1/4]], -4, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-7, [[-7, 1/4], [-4, 1/2], [-1, 1/4]], -4, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
7. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-6,"support":[-6,-5,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-6, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], -5, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-6, [[-6, 1/4], [-5, 1/2], [-4, 1/4]], -5, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
8. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-5,"support":[-5,-3,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-5, [[-5, 1/4], [-3, 1/2], [-1, 1/4]], -3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-5, [[-5, 1/4], [-3, 1/2], [-1, 1/4]], -3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
9. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-4,"support":[-4,-1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-4, [[-4, 1/4], [-1, 1/2], [2, 1/4]], -1, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-4, [[-4, 1/4], [-1, 1/2], [2, 1/4]], -1, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
10. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-3,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-3, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], -2, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-3, [[-3, 1/4], [-2, 1/2], [-1, 1/4]], -2, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
11. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-2,"support":[-2,0,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-2, [[-2, 1/4], [0, 1/2], [2, 1/4]], 0, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-2, [[-2, 1/4], [0, 1/2], [2, 1/4]], 0, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
12. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":-1,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(-1, [[-1, 1/4], [2, 1/2], [5, 1/4]], 2, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(-1, [[-1, 1/4], [2, 1/2], [5, 1/4]], 2, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
13. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":0,"support":[0,1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(0, [[0, 1/4], [1, 1/2], [2, 1/4]], 1, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(0, [[0, 1/4], [1, 1/2], [2, 1/4]], 1, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
14. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":1,"support":[1,3,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(1, [[1, 1/4], [3, 1/2], [5, 1/4]], 3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(1, [[1, 1/4], [3, 1/2], [5, 1/4]], 3, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
15. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":2,"support":[2,5,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(2, [[2, 1/4], [5, 1/2], [8, 1/4]], 5, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(2, [[2, 1/4], [5, 1/2], [8, 1/4]], 5, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
16. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":3,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(3, [[3, 1/4], [4, 1/2], [5, 1/4]], 4, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(3, [[3, 1/4], [4, 1/2], [5, 1/4]], 4, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
17. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":4,"support":[4,6,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(4, [[4, 1/4], [6, 1/2], [8, 1/4]], 6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(4, [[4, 1/4], [6, 1/2], [8, 1/4]], 6, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
18. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":5,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(5, [[5, 1/4], [8, 1/2], [11, 1/4]], 8, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(5, [[5, 1/4], [8, 1/2], [11, 1/4]], 8, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
19. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":6,"support":[6,7,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(6, [[6, 1/4], [7, 1/2], [8, 1/4]], 7, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(6, [[6, 1/4], [7, 1/2], [8, 1/4]], 7, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
20. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":7,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(7, [[7, 1/4], [9, 1/2], [11, 1/4]], 9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(7, [[7, 1/4], [9, 1/2], [11, 1/4]], 9, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
21. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":8,"support":[8,11,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(8, [[8, 1/4], [11, 1/2], [14, 1/4]], 11, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(8, [[8, 1/4], [11, 1/2], [14, 1/4]], 11, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
22. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":9,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(9, [[9, 1/4], [10, 1/2], [11, 1/4]], 10, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(9, [[9, 1/4], [10, 1/2], [11, 1/4]], 10, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
23. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":10,"support":[10,12,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(10, [[10, 1/4], [12, 1/2], [14, 1/4]], 12, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(10, [[10, 1/4], [12, 1/2], [14, 1/4]], 12, 2, 2, 6, 6, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
24. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":11,"support":[11,14,17],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(11, [[11, 1/4], [14, 1/2], [17, 1/4]], 14, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(11, [[11, 1/4], [14, 1/2], [17, 1/4]], 14, 3, 9/2, 27/2, 27/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
25. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-single-theta-identity；資料={"theta":12,"support":[12,13,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [theta, law_rows, mean, bias, variance, MSE, variance_plus_bias_squared, identity_holds, certificate] 欄序回答。
查看答案與解釋
(12, [[12, 1/4], [13, 1/2], [14, 1/4]], 13, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)
Wave6第九層核對=(12, [[12, 1/4], [13, 1/2], [14, 1/4]], 13, 1, 1/2, 3/2, 3/2, 是, MSE_equals_variance_plus_squared_bias_under_one_complete_sampling_law)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-single-theta-identity · candidate
26. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-12,"support":[-11,-10,-9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
27. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-11,"support":[-10,-9,-8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
28. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-10,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
29. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-9,"support":[-8,-7,-6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
30. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-8,"support":[-7,-6,-5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
31. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-7,"support":[-6,-5,-4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
32. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-6,"support":[-5,-4,-3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
33. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-5,"support":[-4,-3,-2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
34. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-4,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
35. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-3,"support":[-2,-1,0],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(-1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(-1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
36. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-2,"support":[-1,0,1],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(0, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(0, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
37. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":-1,"support":[0,1,2],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(1, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
38. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":0,"support":[1,2,3],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(2, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
39. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":1,"support":[2,3,4],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(3, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
40. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":2,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(4, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
41. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":3,"support":[4,5,6],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(5, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
42. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":4,"support":[5,6,7],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(6, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
43. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":5,"support":[6,7,8],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(7, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
44. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":6,"support":[7,8,9],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(8, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
45. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":7,"support":[8,9,10],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(9, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
46. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":8,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(10, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
47. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":9,"support":[10,11,12],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(11, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(11, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
48. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":10,"support":[11,12,13],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(12, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(12, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
49. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":11,"support":[12,13,14],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(13, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(13, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
50. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-cross-term-cancellation；資料={"theta":12,"support":[13,14,15],"probabilities":[[1,4],[1,2],[1,4]]}。請依 [mean, centered_mean, bias, cross_term, cross_term_zero, certificate] 欄序回答。
查看答案與解釋
(14, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)
Wave6第九層核對=(14, 0, 2, 0, 是, E_of_T_minus_E_T_is_zero_so_the_cross_term_vanishes)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-cross-term-cancellation · candidate
51. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-12,[-12,-11,-10],[[1,4],[1,2],[1,4]]],[-11,[-12,-11,-10],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-11, -11, 0, 1/2, 1/2, 1/2, 是], [-12, -11, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-11, -11, 0, 1/2, 1/2, 1/2, 是], [-12, -11, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
52. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-11,[-11,-9,-7],[[1,4],[1,2],[1,4]]],[-10,[-11,-10,-9],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-10, -10, 0, 1/2, 1/2, 1/2, 是], [-11, -9, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-10, -10, 0, 1/2, 1/2, 1/2, 是], [-11, -9, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
53. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-10,[-10,-7,-4],[[1,4],[1,2],[1,4]]],[-9,[-10,-9,-8],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-10, -7, 3, 9/2, 27/2, 27/2, 是], [-9, -9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-10, -7, 3, 9/2, 27/2, 27/2, 是], [-9, -9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
54. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-9,[-9,-8,-7],[[1,4],[1,2],[1,4]]],[-8,[-9,-8,-7],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-8, -8, 0, 1/2, 1/2, 1/2, 是], [-9, -8, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-8, -8, 0, 1/2, 1/2, 1/2, 是], [-9, -8, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
55. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-8,[-8,-6,-4],[[1,4],[1,2],[1,4]]],[-7,[-8,-7,-6],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-7, -7, 0, 1/2, 1/2, 1/2, 是], [-8, -6, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-7, -7, 0, 1/2, 1/2, 1/2, 是], [-8, -6, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
56. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-7,[-7,-4,-1],[[1,4],[1,2],[1,4]]],[-6,[-7,-6,-5],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-6, -6, 0, 1/2, 1/2, 1/2, 是], [-7, -4, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-6, -6, 0, 1/2, 1/2, 1/2, 是], [-7, -4, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
57. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-6,[-6,-5,-4],[[1,4],[1,2],[1,4]]],[-5,[-6,-5,-4],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-5, -5, 0, 1/2, 1/2, 1/2, 是], [-6, -5, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-5, -5, 0, 1/2, 1/2, 1/2, 是], [-6, -5, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
58. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-5,[-5,-3,-1],[[1,4],[1,2],[1,4]]],[-4,[-5,-4,-3],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-4, -4, 0, 1/2, 1/2, 1/2, 是], [-5, -3, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-4, -4, 0, 1/2, 1/2, 1/2, 是], [-5, -3, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
59. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-4,[-4,-1,2],[[1,4],[1,2],[1,4]]],[-3,[-4,-3,-2],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-3, -3, 0, 1/2, 1/2, 1/2, 是], [-4, -1, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-3, -3, 0, 1/2, 1/2, 1/2, 是], [-4, -1, 3, 9/2, 27/2, 27/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
60. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-3,[-3,-2,-1],[[1,4],[1,2],[1,4]]],[-2,[-3,-2,-1],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-2, -2, 0, 1/2, 1/2, 1/2, 是], [-3, -2, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-2, -2, 0, 1/2, 1/2, 1/2, 是], [-3, -2, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
61. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-2,[-2,0,2],[[1,4],[1,2],[1,4]]],[-1,[-2,-1,0],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-1, -1, 0, 1/2, 1/2, 1/2, 是], [-2, 0, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-1, -1, 0, 1/2, 1/2, 1/2, 是], [-2, 0, 2, 2, 6, 6, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
62. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[-1,[-1,2,5],[[1,4],[1,2],[1,4]]],[0,[-1,0,1],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[-1, 2, 3, 9/2, 27/2, 27/2, 是], [0, 0, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[-1, 2, 3, 9/2, 27/2, 27/2, 是], [0, 0, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
63. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[0,[0,1,2],[[1,4],[1,2],[1,4]]],[1,[0,1,2],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[0, 1, 1, 1/2, 3/2, 3/2, 是], [1, 1, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[0, 1, 1, 1/2, 3/2, 3/2, 是], [1, 1, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
64. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[1,[1,3,5],[[1,4],[1,2],[1,4]]],[2,[1,2,3],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[1, 3, 2, 2, 6, 6, 是], [2, 2, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[1, 3, 2, 2, 6, 6, 是], [2, 2, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
65. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[2,[2,5,8],[[1,4],[1,2],[1,4]]],[3,[2,3,4],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[2, 5, 3, 9/2, 27/2, 27/2, 是], [3, 3, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[2, 5, 3, 9/2, 27/2, 27/2, 是], [3, 3, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
66. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[3,[3,4,5],[[1,4],[1,2],[1,4]]],[4,[3,4,5],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[3, 4, 1, 1/2, 3/2, 3/2, 是], [4, 4, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[3, 4, 1, 1/2, 3/2, 3/2, 是], [4, 4, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
67. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[4,[4,6,8],[[1,4],[1,2],[1,4]]],[5,[4,5,6],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[4, 6, 2, 2, 6, 6, 是], [5, 5, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[4, 6, 2, 2, 6, 6, 是], [5, 5, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
68. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[5,[5,8,11],[[1,4],[1,2],[1,4]]],[6,[5,6,7],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[5, 8, 3, 9/2, 27/2, 27/2, 是], [6, 6, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[5, 8, 3, 9/2, 27/2, 27/2, 是], [6, 6, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
69. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[6,[6,7,8],[[1,4],[1,2],[1,4]]],[7,[6,7,8],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[6, 7, 1, 1/2, 3/2, 3/2, 是], [7, 7, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[6, 7, 1, 1/2, 3/2, 3/2, 是], [7, 7, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
70. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[7,[7,9,11],[[1,4],[1,2],[1,4]]],[8,[7,8,9],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[7, 9, 2, 2, 6, 6, 是], [8, 8, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[7, 9, 2, 2, 6, 6, 是], [8, 8, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
71. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[8,[8,11,14],[[1,4],[1,2],[1,4]]],[9,[8,9,10],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[8, 11, 3, 9/2, 27/2, 27/2, 是], [9, 9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[8, 11, 3, 9/2, 27/2, 27/2, 是], [9, 9, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
72. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[9,[9,10,11],[[1,4],[1,2],[1,4]]],[10,[9,10,11],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[10, 10, 0, 1/2, 1/2, 1/2, 是], [9, 10, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[10, 10, 0, 1/2, 1/2, 1/2, 是], [9, 10, 1, 1/2, 3/2, 3/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
73. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[10,[10,12,14],[[1,4],[1,2],[1,4]]],[11,[10,11,12],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[10, 12, 2, 2, 6, 6, 是], [11, 11, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[10, 12, 2, 2, 6, 6, 是], [11, 11, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
74. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[11,[11,14,17],[[1,4],[1,2],[1,4]]],[12,[11,12,13],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[11, 14, 3, 9/2, 27/2, 27/2, 是], [12, 12, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[11, 14, 3, 9/2, 27/2, 27/2, 是], [12, 12, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
75. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-multi-theta-table；資料={"laws":[[12,[12,13,14],[[1,4],[1,2],[1,4]]],[13,[12,13,14],[[1,4],[1,2],[1,4]]]]}。請依 [theta_identity_rows, all_identities_hold, certificate] 欄序回答。
查看答案與解釋
([[12, 13, 1, 1/2, 3/2, 3/2, 是], [13, 13, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)
Wave6第九層核對=([[12, 13, 1, 1/2, 3/2, 3/2, 是], [13, 13, 0, 1/2, 1/2, 1/2, 是]], 是, identity_is_pointwise_in_theta_not_an_asymptotic_claim)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-multi-theta-table · candidate
76. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-12,"support":[-13,-12,-11],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-12, -13, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-12, -13, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
77. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-11,"support":[-11,-9,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-11, -11, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-11, -11, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
78. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-10,"support":[-13,-10,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-13}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-10, -13, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-10, -13, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
79. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-9,"support":[-9,-8,-7],"probabilities":[[1,4],[1,2],[1,4]],"observed":-9}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-9, -9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-9, -9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
80. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-8,"support":[-10,-8,-6],"probabilities":[[1,4],[1,2],[1,4]],"observed":-10}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-8, -10, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-8, -10, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
81. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-7,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-7, -7, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-7, -7, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
82. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-6,"support":[-7,-6,-5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-6, -7, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-6, -7, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
83. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-5,"support":[-5,-3,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-5, -5, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-5, -5, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
84. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-4,"support":[-7,-4,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-4, -7, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-4, -7, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
85. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-3,"support":[-3,-2,-1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-3}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-3, -3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-3, -3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
86. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-2,"support":[-4,-2,0],"probabilities":[[1,4],[1,2],[1,4]],"observed":-4}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-2, -4, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-2, -4, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
87. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":-1,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(-1, -1, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(-1, -1, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
88. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":0,"support":[-1,0,1],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(0, -1, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(0, -1, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
89. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":1,"support":[1,3,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(1, 1, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(1, 1, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
90. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":2,"support":[-1,2,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":-1}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(2, -1, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(2, -1, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
91. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":3,"support":[3,4,5],"probabilities":[[1,4],[1,2],[1,4]],"observed":3}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(3, 3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(3, 3, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
92. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":4,"support":[2,4,6],"probabilities":[[1,4],[1,2],[1,4]],"observed":2}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(4, 2, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(4, 2, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
93. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":5,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(5, 5, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(5, 5, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
94. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":6,"support":[5,6,7],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(6, 5, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(6, 5, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
95. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":7,"support":[7,9,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":7}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(7, 7, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(7, 7, 0, 2, 否, 2, 6, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
96. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":8,"support":[5,8,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":5}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(8, 5, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(8, 5, 9, 0, 是, 9/2, 9/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
97. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":9,"support":[9,10,11],"probabilities":[[1,4],[1,2],[1,4]],"observed":9}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(9, 9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(9, 9, 0, 1, 否, 1/2, 3/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
98. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":10,"support":[8,10,12],"probabilities":[[1,4],[1,2],[1,4]],"observed":8}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(10, 8, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(10, 8, 4, 0, 是, 2, 2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
99. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":11,"support":[11,14,17],"probabilities":[[1,4],[1,2],[1,4]],"observed":11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(11, 11, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(11, 11, 0, 3, 否, 9/2, 27/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
100. 偏誤－變異數分解
逐theta完整finite sampling law上的exact mean、bias、variance與MSE。操作=biasvar-biased-unbiased-boundary；資料={"theta":12,"support":[11,12,13],"probabilities":[[1,4],[1,2],[1,4]],"observed":11}。請依 [theta, observed, observed_squared_error, bias, unbiased, variance, MSE, variance_comparison_holds, unbiased_and_zero_MSE, consistency_claim, boundary] 欄序回答。
variance_comparison_holds在unbiased時驗MSE=variance，否則驗MSE≥variance；單次loss可碰巧等於MSE。最後否不否定這種巧合，不提供consistency。
查看答案與解釋
(12, 11, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)
Wave6第九層核對=(12, 11, 1, 0, 是, 1/2, 1/2, 是, 否, 否, unbiased_only_gives_MSE_equals_variance_not_zero_MSE_or_consistency_and_observed_error_is_not_MSE)；依完整明示資料獨立重算；cross term以E[T-E[T]]=0消去並直接核MSE=variance+bias^2；observed error不是MSE；unbiased只給MSE=variance，不推出zero MSE或consistency。
本題逐步詳解（AI 二次覆核）
偏誤－變異數分解 · qf-mod46-biasvar-biased-unbiased-boundary · candidate
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