有限模型最大似然估計量基礎 · 脈衝 R04
本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261015-advance-20261116-r04-finite-maximum-likelihood-estimator-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. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a0","b0"],"observations":["x0","y0"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x0"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a0, b0], [x0, y0], [[3/4, 1/4], [1/4, 3/4]], x0, [[a0, 3/4], [b0, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a0, b0], [x0, y0], [[3/4, 1/4], [1/4, 3/4]], x0, [[a0, 3/4], [b0, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
2. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a1","b1"],"observations":["x1","y1"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x1"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a1, b1], [x1, y1], [[3/4, 1/4], [1/4, 3/4]], x1, [[a1, 3/4], [b1, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a1, b1], [x1, y1], [[3/4, 1/4], [1/4, 3/4]], x1, [[a1, 3/4], [b1, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
3. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a2","b2"],"observations":["x2","y2"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x2"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a2, b2], [x2, y2], [[3/4, 1/4], [1/4, 3/4]], x2, [[a2, 3/4], [b2, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a2, b2], [x2, y2], [[3/4, 1/4], [1/4, 3/4]], x2, [[a2, 3/4], [b2, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
4. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a3","b3"],"observations":["x3","y3"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x3"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a3, b3], [x3, y3], [[3/4, 1/4], [1/4, 3/4]], x3, [[a3, 3/4], [b3, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a3, b3], [x3, y3], [[3/4, 1/4], [1/4, 3/4]], x3, [[a3, 3/4], [b3, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
5. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a4","b4"],"observations":["x4","y4"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x4"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a4, b4], [x4, y4], [[3/4, 1/4], [1/4, 3/4]], x4, [[a4, 3/4], [b4, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a4, b4], [x4, y4], [[3/4, 1/4], [1/4, 3/4]], x4, [[a4, 3/4], [b4, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
6. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a5","b5"],"observations":["x5","y5"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x5"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a5, b5], [x5, y5], [[3/4, 1/4], [1/4, 3/4]], x5, [[a5, 3/4], [b5, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a5, b5], [x5, y5], [[3/4, 1/4], [1/4, 3/4]], x5, [[a5, 3/4], [b5, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
7. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a6","b6"],"observations":["x6","y6"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x6"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a6, b6], [x6, y6], [[3/4, 1/4], [1/4, 3/4]], x6, [[a6, 3/4], [b6, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a6, b6], [x6, y6], [[3/4, 1/4], [1/4, 3/4]], x6, [[a6, 3/4], [b6, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
8. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a7","b7"],"observations":["x7","y7"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x7"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a7, b7], [x7, y7], [[3/4, 1/4], [1/4, 3/4]], x7, [[a7, 3/4], [b7, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a7, b7], [x7, y7], [[3/4, 1/4], [1/4, 3/4]], x7, [[a7, 3/4], [b7, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
9. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a8","b8"],"observations":["x8","y8"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x8"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a8, b8], [x8, y8], [[3/4, 1/4], [1/4, 3/4]], x8, [[a8, 3/4], [b8, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a8, b8], [x8, y8], [[3/4, 1/4], [1/4, 3/4]], x8, [[a8, 3/4], [b8, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
10. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a9","b9"],"observations":["x9","y9"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x9"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a9, b9], [x9, y9], [[3/4, 1/4], [1/4, 3/4]], x9, [[a9, 3/4], [b9, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a9, b9], [x9, y9], [[3/4, 1/4], [1/4, 3/4]], x9, [[a9, 3/4], [b9, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
11. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a10","b10"],"observations":["x10","y10"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x10"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a10, b10], [x10, y10], [[3/4, 1/4], [1/4, 3/4]], x10, [[a10, 3/4], [b10, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a10, b10], [x10, y10], [[3/4, 1/4], [1/4, 3/4]], x10, [[a10, 3/4], [b10, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
12. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a11","b11"],"observations":["x11","y11"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x11"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a11, b11], [x11, y11], [[3/4, 1/4], [1/4, 3/4]], x11, [[a11, 3/4], [b11, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a11, b11], [x11, y11], [[3/4, 1/4], [1/4, 3/4]], x11, [[a11, 3/4], [b11, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
13. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a12","b12"],"observations":["x12","y12"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x12"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a12, b12], [x12, y12], [[3/4, 1/4], [1/4, 3/4]], x12, [[a12, 3/4], [b12, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a12, b12], [x12, y12], [[3/4, 1/4], [1/4, 3/4]], x12, [[a12, 3/4], [b12, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
14. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a13","b13"],"observations":["x13","y13"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x13"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a13, b13], [x13, y13], [[3/4, 1/4], [1/4, 3/4]], x13, [[a13, 3/4], [b13, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a13, b13], [x13, y13], [[3/4, 1/4], [1/4, 3/4]], x13, [[a13, 3/4], [b13, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
15. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a14","b14"],"observations":["x14","y14"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x14"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a14, b14], [x14, y14], [[3/4, 1/4], [1/4, 3/4]], x14, [[a14, 3/4], [b14, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a14, b14], [x14, y14], [[3/4, 1/4], [1/4, 3/4]], x14, [[a14, 3/4], [b14, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
16. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a15","b15"],"observations":["x15","y15"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x15"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a15, b15], [x15, y15], [[3/4, 1/4], [1/4, 3/4]], x15, [[a15, 3/4], [b15, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a15, b15], [x15, y15], [[3/4, 1/4], [1/4, 3/4]], x15, [[a15, 3/4], [b15, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
17. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a16","b16"],"observations":["x16","y16"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x16"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a16, b16], [x16, y16], [[3/4, 1/4], [1/4, 3/4]], x16, [[a16, 3/4], [b16, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a16, b16], [x16, y16], [[3/4, 1/4], [1/4, 3/4]], x16, [[a16, 3/4], [b16, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
18. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a17","b17"],"observations":["x17","y17"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x17"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a17, b17], [x17, y17], [[3/4, 1/4], [1/4, 3/4]], x17, [[a17, 3/4], [b17, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a17, b17], [x17, y17], [[3/4, 1/4], [1/4, 3/4]], x17, [[a17, 3/4], [b17, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
19. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a18","b18"],"observations":["x18","y18"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x18"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a18, b18], [x18, y18], [[3/4, 1/4], [1/4, 3/4]], x18, [[a18, 3/4], [b18, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a18, b18], [x18, y18], [[3/4, 1/4], [1/4, 3/4]], x18, [[a18, 3/4], [b18, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
20. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a19","b19"],"observations":["x19","y19"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x19"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a19, b19], [x19, y19], [[3/4, 1/4], [1/4, 3/4]], x19, [[a19, 3/4], [b19, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a19, b19], [x19, y19], [[3/4, 1/4], [1/4, 3/4]], x19, [[a19, 3/4], [b19, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
21. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a20","b20"],"observations":["x20","y20"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x20"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a20, b20], [x20, y20], [[3/4, 1/4], [1/4, 3/4]], x20, [[a20, 3/4], [b20, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a20, b20], [x20, y20], [[3/4, 1/4], [1/4, 3/4]], x20, [[a20, 3/4], [b20, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
22. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a21","b21"],"observations":["x21","y21"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x21"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a21, b21], [x21, y21], [[3/4, 1/4], [1/4, 3/4]], x21, [[a21, 3/4], [b21, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a21, b21], [x21, y21], [[3/4, 1/4], [1/4, 3/4]], x21, [[a21, 3/4], [b21, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
23. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a22","b22"],"observations":["x22","y22"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x22"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a22, b22], [x22, y22], [[3/4, 1/4], [1/4, 3/4]], x22, [[a22, 3/4], [b22, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a22, b22], [x22, y22], [[3/4, 1/4], [1/4, 3/4]], x22, [[a22, 3/4], [b22, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
24. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a23","b23"],"observations":["x23","y23"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x23"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a23, b23], [x23, y23], [[3/4, 1/4], [1/4, 3/4]], x23, [[a23, 3/4], [b23, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a23, b23], [x23, y23], [[3/4, 1/4], [1/4, 3/4]], x23, [[a23, 3/4], [b23, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
25. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-law-likelihood；資料={"theta_values":["a24","b24"],"observations":["x24","y24"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x24"}。請依 [theta_values, observations, probability_rows, observed, likelihood_rows, certificate] 欄序回答。
查看答案與解釋
([a24, b24], [x24, y24], [[3/4, 1/4], [1/4, 3/4]], x24, [[a24, 3/4], [b24, 1/4]], complete_normalized_finite_model_likelihood_table)
Wave6第十層核對=([a24, b24], [x24, y24], [[3/4, 1/4], [1/4, 3/4]], x24, [[a24, 3/4], [b24, 1/4]], complete_normalized_finite_model_likelihood_table)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-law-likelihood · candidate
26. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a0","b0"],"observations":["x0","y0"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x0"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x0, [[a0, 3/4], [b0, 1/4]], 3/4, [a0], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x0, [[a0, 3/4], [b0, 1/4]], 3/4, [a0], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
27. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a1","b1"],"observations":["x1","y1"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x1"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x1, [[a1, 3/4], [b1, 1/4]], 3/4, [a1], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x1, [[a1, 3/4], [b1, 1/4]], 3/4, [a1], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
28. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a2","b2"],"observations":["x2","y2"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x2"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x2, [[a2, 3/4], [b2, 1/4]], 3/4, [a2], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x2, [[a2, 3/4], [b2, 1/4]], 3/4, [a2], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
29. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a3","b3"],"observations":["x3","y3"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x3"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x3, [[a3, 3/4], [b3, 1/4]], 3/4, [a3], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x3, [[a3, 3/4], [b3, 1/4]], 3/4, [a3], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
30. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a4","b4"],"observations":["x4","y4"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x4"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x4, [[a4, 3/4], [b4, 1/4]], 3/4, [a4], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x4, [[a4, 3/4], [b4, 1/4]], 3/4, [a4], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
31. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a5","b5"],"observations":["x5","y5"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x5"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x5, [[a5, 3/4], [b5, 1/4]], 3/4, [a5], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x5, [[a5, 3/4], [b5, 1/4]], 3/4, [a5], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
32. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a6","b6"],"observations":["x6","y6"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x6"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x6, [[a6, 3/4], [b6, 1/4]], 3/4, [a6], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x6, [[a6, 3/4], [b6, 1/4]], 3/4, [a6], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
33. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a7","b7"],"observations":["x7","y7"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x7"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x7, [[a7, 3/4], [b7, 1/4]], 3/4, [a7], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x7, [[a7, 3/4], [b7, 1/4]], 3/4, [a7], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
34. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a8","b8"],"observations":["x8","y8"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x8"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x8, [[a8, 3/4], [b8, 1/4]], 3/4, [a8], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x8, [[a8, 3/4], [b8, 1/4]], 3/4, [a8], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
35. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a9","b9"],"observations":["x9","y9"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x9"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x9, [[a9, 3/4], [b9, 1/4]], 3/4, [a9], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x9, [[a9, 3/4], [b9, 1/4]], 3/4, [a9], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
36. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a10","b10"],"observations":["x10","y10"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x10"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x10, [[a10, 3/4], [b10, 1/4]], 3/4, [a10], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x10, [[a10, 3/4], [b10, 1/4]], 3/4, [a10], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
37. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a11","b11"],"observations":["x11","y11"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x11"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x11, [[a11, 3/4], [b11, 1/4]], 3/4, [a11], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x11, [[a11, 3/4], [b11, 1/4]], 3/4, [a11], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
38. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a12","b12"],"observations":["x12","y12"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x12"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x12, [[a12, 3/4], [b12, 1/4]], 3/4, [a12], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x12, [[a12, 3/4], [b12, 1/4]], 3/4, [a12], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
39. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a13","b13"],"observations":["x13","y13"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x13"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x13, [[a13, 3/4], [b13, 1/4]], 3/4, [a13], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x13, [[a13, 3/4], [b13, 1/4]], 3/4, [a13], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
40. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a14","b14"],"observations":["x14","y14"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x14"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x14, [[a14, 3/4], [b14, 1/4]], 3/4, [a14], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x14, [[a14, 3/4], [b14, 1/4]], 3/4, [a14], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
41. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a15","b15"],"observations":["x15","y15"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x15"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x15, [[a15, 3/4], [b15, 1/4]], 3/4, [a15], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x15, [[a15, 3/4], [b15, 1/4]], 3/4, [a15], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
42. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a16","b16"],"observations":["x16","y16"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x16"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x16, [[a16, 3/4], [b16, 1/4]], 3/4, [a16], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x16, [[a16, 3/4], [b16, 1/4]], 3/4, [a16], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
43. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a17","b17"],"observations":["x17","y17"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x17"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x17, [[a17, 3/4], [b17, 1/4]], 3/4, [a17], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x17, [[a17, 3/4], [b17, 1/4]], 3/4, [a17], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
44. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a18","b18"],"observations":["x18","y18"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x18"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x18, [[a18, 3/4], [b18, 1/4]], 3/4, [a18], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x18, [[a18, 3/4], [b18, 1/4]], 3/4, [a18], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
45. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a19","b19"],"observations":["x19","y19"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x19"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x19, [[a19, 3/4], [b19, 1/4]], 3/4, [a19], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x19, [[a19, 3/4], [b19, 1/4]], 3/4, [a19], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
46. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a20","b20"],"observations":["x20","y20"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x20"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x20, [[a20, 3/4], [b20, 1/4]], 3/4, [a20], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x20, [[a20, 3/4], [b20, 1/4]], 3/4, [a20], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
47. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a21","b21"],"observations":["x21","y21"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x21"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x21, [[a21, 3/4], [b21, 1/4]], 3/4, [a21], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x21, [[a21, 3/4], [b21, 1/4]], 3/4, [a21], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
48. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a22","b22"],"observations":["x22","y22"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x22"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x22, [[a22, 3/4], [b22, 1/4]], 3/4, [a22], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x22, [[a22, 3/4], [b22, 1/4]], 3/4, [a22], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
49. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a23","b23"],"observations":["x23","y23"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x23"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x23, [[a23, 3/4], [b23, 1/4]], 3/4, [a23], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x23, [[a23, 3/4], [b23, 1/4]], 3/4, [a23], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
50. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-argmax；資料={"theta_values":["a24","b24"],"observations":["x24","y24"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"observed":"x24"}。請依 [observed, likelihood_rows, maximum_likelihood, argmax_parameters, unique_argmax, certificate] 欄序回答。
查看答案與解釋
(x24, [[a24, 3/4], [b24, 1/4]], 3/4, [a24], 是, MLE_argmax_need_not_be_unique)
Wave6第十層核對=(x24, [[a24, 3/4], [b24, 1/4]], 3/4, [a24], 是, MLE_argmax_need_not_be_unique)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-argmax · candidate
51. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a0","b0"],"observations":["x0","y0"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a0","b0"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a0, b0], [[x0, [a0], a0], [y0, [b0], b0]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a0, b0], [[x0, [a0], a0], [y0, [b0], b0]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
52. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a1","b1"],"observations":["x1","y1"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a1","b1"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a1, b1], [[x1, [a1], a1], [y1, [b1], b1]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a1, b1], [[x1, [a1], a1], [y1, [b1], b1]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
53. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a2","b2"],"observations":["x2","y2"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a2","b2"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a2, b2], [[x2, [a2], a2], [y2, [b2], b2]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a2, b2], [[x2, [a2], a2], [y2, [b2], b2]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
54. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a3","b3"],"observations":["x3","y3"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a3","b3"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a3, b3], [[x3, [a3], a3], [y3, [b3], b3]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a3, b3], [[x3, [a3], a3], [y3, [b3], b3]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
55. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a4","b4"],"observations":["x4","y4"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a4","b4"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a4, b4], [[x4, [a4], a4], [y4, [b4], b4]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a4, b4], [[x4, [a4], a4], [y4, [b4], b4]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
56. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a5","b5"],"observations":["x5","y5"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a5","b5"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a5, b5], [[x5, [a5], a5], [y5, [b5], b5]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a5, b5], [[x5, [a5], a5], [y5, [b5], b5]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
57. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a6","b6"],"observations":["x6","y6"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a6","b6"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a6, b6], [[x6, [a6], a6], [y6, [b6], b6]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a6, b6], [[x6, [a6], a6], [y6, [b6], b6]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
58. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a7","b7"],"observations":["x7","y7"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a7","b7"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a7, b7], [[x7, [a7], a7], [y7, [b7], b7]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a7, b7], [[x7, [a7], a7], [y7, [b7], b7]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
59. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a8","b8"],"observations":["x8","y8"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a8","b8"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a8, b8], [[x8, [a8], a8], [y8, [b8], b8]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a8, b8], [[x8, [a8], a8], [y8, [b8], b8]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
60. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a9","b9"],"observations":["x9","y9"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a9","b9"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a9, b9], [[x9, [a9], a9], [y9, [b9], b9]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a9, b9], [[x9, [a9], a9], [y9, [b9], b9]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
61. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a10","b10"],"observations":["x10","y10"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a10","b10"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a10, b10], [[x10, [a10], a10], [y10, [b10], b10]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a10, b10], [[x10, [a10], a10], [y10, [b10], b10]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
62. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a11","b11"],"observations":["x11","y11"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a11","b11"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a11, b11], [[x11, [a11], a11], [y11, [b11], b11]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a11, b11], [[x11, [a11], a11], [y11, [b11], b11]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
63. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a12","b12"],"observations":["x12","y12"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a12","b12"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a12, b12], [[x12, [a12], a12], [y12, [b12], b12]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a12, b12], [[x12, [a12], a12], [y12, [b12], b12]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
64. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a13","b13"],"observations":["x13","y13"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a13","b13"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a13, b13], [[x13, [a13], a13], [y13, [b13], b13]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a13, b13], [[x13, [a13], a13], [y13, [b13], b13]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
65. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a14","b14"],"observations":["x14","y14"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a14","b14"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a14, b14], [[x14, [a14], a14], [y14, [b14], b14]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a14, b14], [[x14, [a14], a14], [y14, [b14], b14]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
66. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a15","b15"],"observations":["x15","y15"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a15","b15"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a15, b15], [[x15, [a15], a15], [y15, [b15], b15]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a15, b15], [[x15, [a15], a15], [y15, [b15], b15]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
67. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a16","b16"],"observations":["x16","y16"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a16","b16"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a16, b16], [[x16, [a16], a16], [y16, [b16], b16]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a16, b16], [[x16, [a16], a16], [y16, [b16], b16]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
68. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a17","b17"],"observations":["x17","y17"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a17","b17"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a17, b17], [[x17, [a17], a17], [y17, [b17], b17]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a17, b17], [[x17, [a17], a17], [y17, [b17], b17]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
69. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a18","b18"],"observations":["x18","y18"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a18","b18"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a18, b18], [[x18, [a18], a18], [y18, [b18], b18]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a18, b18], [[x18, [a18], a18], [y18, [b18], b18]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
70. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a19","b19"],"observations":["x19","y19"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a19","b19"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a19, b19], [[x19, [a19], a19], [y19, [b19], b19]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a19, b19], [[x19, [a19], a19], [y19, [b19], b19]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
71. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a20","b20"],"observations":["x20","y20"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a20","b20"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a20, b20], [[x20, [a20], a20], [y20, [b20], b20]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a20, b20], [[x20, [a20], a20], [y20, [b20], b20]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
72. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a21","b21"],"observations":["x21","y21"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a21","b21"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a21, b21], [[x21, [a21], a21], [y21, [b21], b21]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a21, b21], [[x21, [a21], a21], [y21, [b21], b21]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
73. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a22","b22"],"observations":["x22","y22"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a22","b22"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a22, b22], [[x22, [a22], a22], [y22, [b22], b22]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a22, b22], [[x22, [a22], a22], [y22, [b22], b22]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
74. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a23","b23"],"observations":["x23","y23"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a23","b23"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a23, b23], [[x23, [a23], a23], [y23, [b23], b23]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a23, b23], [[x23, [a23], a23], [y23, [b23], b23]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
75. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-total-tie-estimator；資料={"theta_values":["a24","b24"],"observations":["x24","y24"],"probability_rows":[[[3,4],[1,4]],[[1,4],[3,4]]],"tie_order":["a24","b24"]}。請依 [tie_order, estimator_rows, total_estimator, certificate] 欄序回答。
查看答案與解釋
([a24, b24], [[x24, [a24], a24], [y24, [b24], b24]], 是, theta_independent_tie_rule_makes_a_total_estimator)
Wave6第十層核對=([a24, b24], [[x24, [a24], a24], [y24, [b24], b24]], 是, theta_independent_tie_rule_makes_a_total_estimator)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-total-tie-estimator · candidate
76. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a0","b0"],"observations":["x0","y0"],"probability_rows":[[0,1],[0,1]],"observed":"x0","tie_order":["a0","b0"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x0, [[a0, 0], [b0, 0]], 0, [a0, b0], [a0, b0], [x0, [a0, b0], a0], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x0, [[a0, 0], [b0, 0]], 0, [a0, b0], [a0, b0], [x0, [a0, b0], a0], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
77. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a1","b1"],"observations":["x1","y1"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x1","tie_order":["a1","b1"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x1, [[a1, 1/2], [b1, 1/2]], 1/2, [a1, b1], [a1, b1], [x1, [a1, b1], a1], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x1, [[a1, 1/2], [b1, 1/2]], 1/2, [a1, b1], [a1, b1], [x1, [a1, b1], a1], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
78. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a2","b2"],"observations":["x2","y2"],"probability_rows":[[0,1],[0,1]],"observed":"x2","tie_order":["a2","b2"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x2, [[a2, 0], [b2, 0]], 0, [a2, b2], [a2, b2], [x2, [a2, b2], a2], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x2, [[a2, 0], [b2, 0]], 0, [a2, b2], [a2, b2], [x2, [a2, b2], a2], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
79. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a3","b3"],"observations":["x3","y3"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x3","tie_order":["a3","b3"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x3, [[a3, 1/2], [b3, 1/2]], 1/2, [a3, b3], [a3, b3], [x3, [a3, b3], a3], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x3, [[a3, 1/2], [b3, 1/2]], 1/2, [a3, b3], [a3, b3], [x3, [a3, b3], a3], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
80. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a4","b4"],"observations":["x4","y4"],"probability_rows":[[0,1],[0,1]],"observed":"x4","tie_order":["a4","b4"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x4, [[a4, 0], [b4, 0]], 0, [a4, b4], [a4, b4], [x4, [a4, b4], a4], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x4, [[a4, 0], [b4, 0]], 0, [a4, b4], [a4, b4], [x4, [a4, b4], a4], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
81. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a5","b5"],"observations":["x5","y5"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x5","tie_order":["a5","b5"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x5, [[a5, 1/2], [b5, 1/2]], 1/2, [a5, b5], [a5, b5], [x5, [a5, b5], a5], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x5, [[a5, 1/2], [b5, 1/2]], 1/2, [a5, b5], [a5, b5], [x5, [a5, b5], a5], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
82. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a6","b6"],"observations":["x6","y6"],"probability_rows":[[0,1],[0,1]],"observed":"x6","tie_order":["a6","b6"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x6, [[a6, 0], [b6, 0]], 0, [a6, b6], [a6, b6], [x6, [a6, b6], a6], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x6, [[a6, 0], [b6, 0]], 0, [a6, b6], [a6, b6], [x6, [a6, b6], a6], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
83. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a7","b7"],"observations":["x7","y7"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x7","tie_order":["a7","b7"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x7, [[a7, 1/2], [b7, 1/2]], 1/2, [a7, b7], [a7, b7], [x7, [a7, b7], a7], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x7, [[a7, 1/2], [b7, 1/2]], 1/2, [a7, b7], [a7, b7], [x7, [a7, b7], a7], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
84. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a8","b8"],"observations":["x8","y8"],"probability_rows":[[0,1],[0,1]],"observed":"x8","tie_order":["a8","b8"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x8, [[a8, 0], [b8, 0]], 0, [a8, b8], [a8, b8], [x8, [a8, b8], a8], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x8, [[a8, 0], [b8, 0]], 0, [a8, b8], [a8, b8], [x8, [a8, b8], a8], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
85. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a9","b9"],"observations":["x9","y9"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x9","tie_order":["a9","b9"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x9, [[a9, 1/2], [b9, 1/2]], 1/2, [a9, b9], [a9, b9], [x9, [a9, b9], a9], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x9, [[a9, 1/2], [b9, 1/2]], 1/2, [a9, b9], [a9, b9], [x9, [a9, b9], a9], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
86. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a10","b10"],"observations":["x10","y10"],"probability_rows":[[0,1],[0,1]],"observed":"x10","tie_order":["a10","b10"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x10, [[a10, 0], [b10, 0]], 0, [a10, b10], [a10, b10], [x10, [a10, b10], a10], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x10, [[a10, 0], [b10, 0]], 0, [a10, b10], [a10, b10], [x10, [a10, b10], a10], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
87. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a11","b11"],"observations":["x11","y11"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x11","tie_order":["a11","b11"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x11, [[a11, 1/2], [b11, 1/2]], 1/2, [a11, b11], [a11, b11], [x11, [a11, b11], a11], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x11, [[a11, 1/2], [b11, 1/2]], 1/2, [a11, b11], [a11, b11], [x11, [a11, b11], a11], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
88. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a12","b12"],"observations":["x12","y12"],"probability_rows":[[0,1],[0,1]],"observed":"x12","tie_order":["a12","b12"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x12, [[a12, 0], [b12, 0]], 0, [a12, b12], [a12, b12], [x12, [a12, b12], a12], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x12, [[a12, 0], [b12, 0]], 0, [a12, b12], [a12, b12], [x12, [a12, b12], a12], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
89. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a13","b13"],"observations":["x13","y13"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x13","tie_order":["a13","b13"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x13, [[a13, 1/2], [b13, 1/2]], 1/2, [a13, b13], [a13, b13], [x13, [a13, b13], a13], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x13, [[a13, 1/2], [b13, 1/2]], 1/2, [a13, b13], [a13, b13], [x13, [a13, b13], a13], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
90. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a14","b14"],"observations":["x14","y14"],"probability_rows":[[0,1],[0,1]],"observed":"x14","tie_order":["a14","b14"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x14, [[a14, 0], [b14, 0]], 0, [a14, b14], [a14, b14], [x14, [a14, b14], a14], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x14, [[a14, 0], [b14, 0]], 0, [a14, b14], [a14, b14], [x14, [a14, b14], a14], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
91. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a15","b15"],"observations":["x15","y15"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x15","tie_order":["a15","b15"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x15, [[a15, 1/2], [b15, 1/2]], 1/2, [a15, b15], [a15, b15], [x15, [a15, b15], a15], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x15, [[a15, 1/2], [b15, 1/2]], 1/2, [a15, b15], [a15, b15], [x15, [a15, b15], a15], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
92. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a16","b16"],"observations":["x16","y16"],"probability_rows":[[0,1],[0,1]],"observed":"x16","tie_order":["a16","b16"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x16, [[a16, 0], [b16, 0]], 0, [a16, b16], [a16, b16], [x16, [a16, b16], a16], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x16, [[a16, 0], [b16, 0]], 0, [a16, b16], [a16, b16], [x16, [a16, b16], a16], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
93. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a17","b17"],"observations":["x17","y17"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x17","tie_order":["a17","b17"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x17, [[a17, 1/2], [b17, 1/2]], 1/2, [a17, b17], [a17, b17], [x17, [a17, b17], a17], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x17, [[a17, 1/2], [b17, 1/2]], 1/2, [a17, b17], [a17, b17], [x17, [a17, b17], a17], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
94. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a18","b18"],"observations":["x18","y18"],"probability_rows":[[0,1],[0,1]],"observed":"x18","tie_order":["a18","b18"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x18, [[a18, 0], [b18, 0]], 0, [a18, b18], [a18, b18], [x18, [a18, b18], a18], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x18, [[a18, 0], [b18, 0]], 0, [a18, b18], [a18, b18], [x18, [a18, b18], a18], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
95. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a19","b19"],"observations":["x19","y19"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x19","tie_order":["a19","b19"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x19, [[a19, 1/2], [b19, 1/2]], 1/2, [a19, b19], [a19, b19], [x19, [a19, b19], a19], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x19, [[a19, 1/2], [b19, 1/2]], 1/2, [a19, b19], [a19, b19], [x19, [a19, b19], a19], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
96. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a20","b20"],"observations":["x20","y20"],"probability_rows":[[0,1],[0,1]],"observed":"x20","tie_order":["a20","b20"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x20, [[a20, 0], [b20, 0]], 0, [a20, b20], [a20, b20], [x20, [a20, b20], a20], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x20, [[a20, 0], [b20, 0]], 0, [a20, b20], [a20, b20], [x20, [a20, b20], a20], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
97. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a21","b21"],"observations":["x21","y21"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x21","tie_order":["a21","b21"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x21, [[a21, 1/2], [b21, 1/2]], 1/2, [a21, b21], [a21, b21], [x21, [a21, b21], a21], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x21, [[a21, 1/2], [b21, 1/2]], 1/2, [a21, b21], [a21, b21], [x21, [a21, b21], a21], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
98. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a22","b22"],"observations":["x22","y22"],"probability_rows":[[0,1],[0,1]],"observed":"x22","tie_order":["a22","b22"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x22, [[a22, 0], [b22, 0]], 0, [a22, b22], [a22, b22], [x22, [a22, b22], a22], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x22, [[a22, 0], [b22, 0]], 0, [a22, b22], [a22, b22], [x22, [a22, b22], a22], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
99. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"tie","theta_values":["a23","b23"],"observations":["x23","y23"],"probability_rows":[[[1,2],[1,2]],[[1,2],[1,2]]],"observed":"x23","tie_order":["a23","b23"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(tie, x23, [[a23, 1/2], [b23, 1/2]], 1/2, [a23, b23], [a23, b23], [x23, [a23, b23], a23], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(tie, x23, [[a23, 1/2], [b23, 1/2]], 1/2, [a23, b23], [a23, b23], [x23, [a23, b23], a23], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
100. 有限模型最大似然估計量
完整finite parametric laws、observed likelihood與全部argmax責任。操作=mle-boundary；資料={"mode":"all_zero_likelihood","theta_values":["a24","b24"],"observations":["x24","y24"],"probability_rows":[[0,1],[0,1]],"observed":"x24","tie_order":["a24","b24"]}。請依 [mode, observed, likelihood_rows, maximum_likelihood, argmax_parameters, tie_order, selected_estimator_row, posterior_or_quality_claim, boundary] 欄序回答。
all-zero likelihood對全部theta皆為0時，argmax仍是全部theta，固定tie rule仍給total值；不捏造posterior或估計品質。
查看答案與解釋
(all_zero_likelihood, x24, [[a24, 0], [b24, 0]], 0, [a24, b24], [a24, b24], [x24, [a24, b24], a24], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)
Wave6第十層核對=(all_zero_likelihood, x24, [[a24, 0], [b24, 0]], 0, [a24, b24], [a24, b24], [x24, [a24, b24], a24], 否, MLE_maximizes_likelihood_not_posterior_and_does_not_imply_unbiased_consistent_or_asymptotically_optimal)；依完整明示資料獨立重算；theta-independent deterministic tie rule形成total estimator；MLE不是posterior且不假設unique或推出unbiased/consistent/asymptotic claims。
本題逐步詳解（AI 二次覆核）
有限模型最大似然估計量 · qf-mod47-mle-boundary · candidate
原始題目 JSONL · 驗收報告