第 27119 題：有限模型信賴區間覆蓋率

原題與已知條件

完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]}}。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-finite-confidence-interval-coverage

逐步推導

source roles = [ci-interpretation-boundary]

derived = [[mode, selected_samples, unconditional_coverage_table, selected_mass_and_conditional_coverage_by_theta, unchanged_coverage_without_recomputation_claim, boundary]]

source roles = [[0, 1], [a, b], [[[19, 21], [2, 21]], [[2, 21], [19, 21]]], [[0, 0], [1, 1]]]

derived = [[0, 1], [a, b], [[0, 0], [1, 1]], [[19/21, 2/21], [2/21, 19/21]], [[a, [0, 0], 0], [b, [1, 1], 1]]]

CI theta0 ORIGINAL probability normalization column0 := sum(0, 19/21)

CI theta0 ORIGINAL probability normalization column0 = 19/21

CI theta0 ORIGINAL probability normalization column1 := sum(19/21, 2/21)

CI theta0 ORIGINAL probability normalization column1 = 1

CI theta1 ORIGINAL probability normalization column0 := sum(0, 2/21)

CI theta1 ORIGINAL probability normalization column0 = 2/21

CI theta1 ORIGINAL probability normalization column1 := sum(2/21, 19/21)

CI theta1 ORIGINAL probability normalization column1 = 1

CI theta0 ORIGINAL included coverage column0 := sum(0, 19/21)

CI theta0 ORIGINAL included coverage column0 = 19/21

source roles = [0, [a, b], [[0, 0], [1, 1]], [19/21, 2/21]]

derived = [[[a, 0, 0, 0, 是, 19/21], [b, 1, 1, 0, 否, 2/21]], 19/21]

CI theta1 ORIGINAL included coverage column1 := sum(0, 19/21)

CI theta1 ORIGINAL included coverage column1 = 19/21

source roles = [1, [a, b], [[0, 0], [1, 1]], [2/21, 19/21]]

derived = [[[a, 0, 0, 1, 否, 2/21], [b, 1, 1, 1, 是, 19/21]], 19/21]

CI theta0 ORIGINAL selected mass column0 := sum(0, 19/21)

CI theta0 ORIGINAL selected mass column0 = 19/21

CI theta0 ORIGINAL selected hit column0 := sum(0, 19/21)

CI theta0 ORIGINAL selected hit column0 = 19/21

CI theta0 ORIGINAL selected conditional coverage := div(19/21, 19/21)

CI theta0 ORIGINAL selected conditional coverage = 1

source roles = [0, [a], 19/21, 19/21]

derived = [1]

CI theta1 ORIGINAL selected mass column0 := sum(0, 2/21)

CI theta1 ORIGINAL selected mass column0 = 2/21

CI theta1 ORIGINAL selected conditional coverage := div(0, 2/21)

CI theta1 ORIGINAL selected conditional coverage = 0

source roles = [1, [a], 2/21, 0]

derived = [0]

source roles = [[a], [[0, 19/21], [1, 19/21]]]

derived = [[a], [[0, 19/21, 1], [1, 2/21, 0]], 否]

逐步反向核對

• S018 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S017 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S016 · premise_and_result_audit — 以精確有理數重算 CI theta1 ORIGINAL selected conditional coverage，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 CI theta1 ORIGINAL selected mass column0，不以小數近似替代。
• S014 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S013 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL selected conditional coverage，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL selected hit column0，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL selected mass column0，不以小數近似替代。
• S010 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S009 · premise_and_result_audit — 以精確有理數重算 CI theta1 ORIGINAL included coverage column1，不以小數近似替代。
• S008 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S007 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL included coverage column0，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 CI theta1 ORIGINAL probability normalization column1，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 CI theta1 ORIGINAL probability normalization column0，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL probability normalization column1，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 CI theta0 ORIGINAL probability normalization column0，不以小數近似替代。
• S002 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。
• S001 · premise_and_result_audit — 回查原始完整資料、步驟操作數與本步前提；有限核對、條件式定理引用與一般形式證明分開。

結論

(ignored_selection, [a], [[0, 19/21], [1, 19/21]], [[0, 19/21, 1], [1, 2/21, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)

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。