第 19158 題：抽樣分布

原題與已知條件

共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 共同有限樣本空間、逐theta模型law與單一theta-independent total statistic。操作=sampling-property-nonconclusion；資料={"parameter_count":2,"outcome_count":4,"laws":[[[1,15],[2,15],[3,15],[9,15]],[[2,19],[3,19],[4,19],[10,19]]],"statistic":[0,0,8,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-sampling-distribution

逐步推導

source operation=sampling-property-nonconclusion;original snapshot and mathematics retained

explicit ordered source output fields=[statistic, claim_marker_1, claim_marker_2, claim_marker_3, claim_marker_4, boundary]

sampling parameter0 full law mass := sum(1/15, 2/15, 1/5, 3/5)

sampling parameter0 full law mass = 1

sampling:original parameter SLOT=0;same outcome carrier Fin(4);ALL aligned law masses=[1/15, 2/15, 1/5, 3/5]

full sum=1;all masses nonnegative=是;qualified probability law;zero-mass outcomes retained

sampling parameter1 full law mass := sum(2/19, 3/19, 4/19, 10/19)

sampling parameter1 full law mass = 1

sampling:original parameter SLOT=1;same outcome carrier Fin(4);ALL aligned law masses=[2/19, 3/19, 4/19, 10/19]

full sum=1;all masses nonnegative=是;qualified probability law;zero-mass outcomes retained

sampling:parameter SLOT carrier Fin(2);common outcome carrier Fin(4);ONE total original statistic array=[0, 0, 8, 9]

T takes only the observation index,not the unknown parameter;SAME function at all parameter slots;its sampling law may still vary with the slot

same total statistic=[0, 0, 8, 9];all parameter laws qualified;no target/asymptotic sequence/prior supplied

four literal No markers WITHHOLD statistical,likelihood and posterior claims;not four named tests or proved negations

逐步反向核對

• S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S006 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S004 · premise_and_result_audit — 以精確有理數重算 sampling parameter1 full law mass，不以小數近似替代。
• S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• S002 · premise_and_result_audit — 以精確有理數重算 sampling parameter0 full law mass，不以小數近似替代。
• S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。

結論

([0, 0, 8, 9], 否, 否, 否, 否, no_unbiased_low_variance_consistency_likelihood_or_posterior_claim)

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。