第 27614 題：有限值IID強大數律

原題與已知條件

無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 無限IID process certificate、finite marginal law與almost-sure limit責任。操作=slln-fixed-n-deviation；資料={"values":[1,2],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":3,"epsilon":[2,4]}。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-strong-law-large-numbers-finite-valued-iid

逐步推導

source roles = [slln-fixed-n-deviation]

derived = [[n, common_mean, epsilon, deviating_joint_word_count, deviation_probability, event_scope, almost_sure_limit_proof_claim, boundary]]

source roles = [infinite_iid]

derived = [ASSUME whole infinite sequence is IID with this common marginal]

SLLN ORIGINAL common marginal ORIGINAL mass sum0 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mass sum0 = 1/2

SLLN ORIGINAL common marginal ORIGINAL mass sum1 := sum(1/2, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mass sum1 = 1

SLLN ORIGINAL common marginal ORIGINAL weighted value0 := mul(1, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted value0 = 1/2

SLLN ORIGINAL common marginal ORIGINAL mean sum0 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL mean sum0 = 1/2

SLLN ORIGINAL common marginal exact unbounded value square0 := mul(1, 1)

SLLN ORIGINAL common marginal exact unbounded value square0 = 1

SLLN ORIGINAL common marginal ORIGINAL weighted square0 := mul(1, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted square0 = 1/2

SLLN ORIGINAL common marginal ORIGINAL second moment sum0 := sum(0, 1/2)

SLLN ORIGINAL common marginal ORIGINAL second moment sum0 = 1/2

SLLN ORIGINAL common marginal ORIGINAL weighted value1 := mul(2, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted value1 = 1

SLLN ORIGINAL common marginal ORIGINAL mean sum1 := sum(1/2, 1)

SLLN ORIGINAL common marginal ORIGINAL mean sum1 = 3/2

SLLN ORIGINAL common marginal exact unbounded value square1 := mul(2, 2)

SLLN ORIGINAL common marginal exact unbounded value square1 = 4

SLLN ORIGINAL common marginal ORIGINAL weighted square1 := mul(4, 1/2)

SLLN ORIGINAL common marginal ORIGINAL weighted square1 = 2

SLLN ORIGINAL common marginal ORIGINAL second moment sum1 := sum(1/2, 2)

SLLN ORIGINAL common marginal ORIGINAL second moment sum1 = 5/2

SLLN ORIGINAL common marginal ORIGINAL mean squared := mul(3/2, 3/2)

SLLN ORIGINAL common marginal ORIGINAL mean squared = 9/4

SLLN ORIGINAL common marginal ORIGINAL second minus mean squared := sub(5/2, 9/4)

SLLN ORIGINAL common marginal ORIGINAL second minus mean squared = 1/4

source roles = [SLLN ORIGINAL common marginal, [1, 2], [[1, 2], [1, 2]]]

derived = [[[1, 1/2], [2, 1/2]], 1, 3/2, 5/2, 1/4]

SLLN ORIGINAL joint word0 integer sum := sum(1, 1, 1)

SLLN ORIGINAL joint word0 integer sum = 3

SLLN ORIGINAL joint word0 mean := div(3, 3)

SLLN ORIGINAL joint word0 mean = 1

SLLN ORIGINAL joint word0 mean minus mu := sub(1, 3/2)

SLLN ORIGINAL joint word0 mean minus mu = -1/2

SLLN ORIGINAL deviating word0 probability factor0 := mul(1, 1/2)

SLLN ORIGINAL deviating word0 probability factor0 = 1/2

SLLN ORIGINAL deviating word0 probability factor1 := mul(1/2, 1/2)

SLLN ORIGINAL deviating word0 probability factor1 = 1/4

SLLN ORIGINAL deviating word0 probability factor2 := mul(1/4, 1/2)

SLLN ORIGINAL deviating word0 probability factor2 = 1/8

SLLN ORIGINAL deviation probability word0 := sum(0, 1/8)

SLLN ORIGINAL deviation probability word0 = 1/8

source roles = [3, 0, [1, 1, 1], 3/2, 1/2]

derived = [1, 1/2, 是, 1/8, 1, 1/8]

SLLN ORIGINAL joint word1 integer sum := sum(1, 1, 2)

SLLN ORIGINAL joint word1 integer sum = 4

SLLN ORIGINAL joint word1 mean := div(4, 3)

SLLN ORIGINAL joint word1 mean = 4/3

SLLN ORIGINAL joint word1 mean minus mu := sub(4/3, 3/2)

SLLN ORIGINAL joint word1 mean minus mu = -1/6

source roles = [3, 1, [1, 1, 2], 3/2, 1/2]

derived = [4/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word2 integer sum := sum(1, 2, 1)

SLLN ORIGINAL joint word2 integer sum = 4

SLLN ORIGINAL joint word2 mean := div(4, 3)

SLLN ORIGINAL joint word2 mean = 4/3

SLLN ORIGINAL joint word2 mean minus mu := sub(4/3, 3/2)

SLLN ORIGINAL joint word2 mean minus mu = -1/6

source roles = [3, 2, [1, 2, 1], 3/2, 1/2]

derived = [4/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word3 integer sum := sum(1, 2, 2)

SLLN ORIGINAL joint word3 integer sum = 5

SLLN ORIGINAL joint word3 mean := div(5, 3)

SLLN ORIGINAL joint word3 mean = 5/3

SLLN ORIGINAL joint word3 mean minus mu := sub(5/3, 3/2)

SLLN ORIGINAL joint word3 mean minus mu = 1/6

source roles = [3, 3, [1, 2, 2], 3/2, 1/2]

derived = [5/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word4 integer sum := sum(2, 1, 1)

SLLN ORIGINAL joint word4 integer sum = 4

SLLN ORIGINAL joint word4 mean := div(4, 3)

SLLN ORIGINAL joint word4 mean = 4/3

SLLN ORIGINAL joint word4 mean minus mu := sub(4/3, 3/2)

SLLN ORIGINAL joint word4 mean minus mu = -1/6

source roles = [3, 4, [2, 1, 1], 3/2, 1/2]

derived = [4/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word5 integer sum := sum(2, 1, 2)

SLLN ORIGINAL joint word5 integer sum = 5

SLLN ORIGINAL joint word5 mean := div(5, 3)

SLLN ORIGINAL joint word5 mean = 5/3

SLLN ORIGINAL joint word5 mean minus mu := sub(5/3, 3/2)

SLLN ORIGINAL joint word5 mean minus mu = 1/6

source roles = [3, 5, [2, 1, 2], 3/2, 1/2]

derived = [5/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word6 integer sum := sum(2, 2, 1)

SLLN ORIGINAL joint word6 integer sum = 5

SLLN ORIGINAL joint word6 mean := div(5, 3)

SLLN ORIGINAL joint word6 mean = 5/3

SLLN ORIGINAL joint word6 mean minus mu := sub(5/3, 3/2)

SLLN ORIGINAL joint word6 mean minus mu = 1/6

source roles = [3, 6, [2, 2, 1], 3/2, 1/2]

derived = [5/3, 1/6, 否, null, 1, 1/8]

SLLN ORIGINAL joint word7 integer sum := sum(2, 2, 2)

SLLN ORIGINAL joint word7 integer sum = 6

SLLN ORIGINAL joint word7 mean := div(6, 3)

SLLN ORIGINAL joint word7 mean = 2

SLLN ORIGINAL joint word7 mean minus mu := sub(2, 3/2)

SLLN ORIGINAL joint word7 mean minus mu = 1/2

SLLN ORIGINAL deviating word7 probability factor0 := mul(1, 1/2)

SLLN ORIGINAL deviating word7 probability factor0 = 1/2

SLLN ORIGINAL deviating word7 probability factor1 := mul(1/2, 1/2)

SLLN ORIGINAL deviating word7 probability factor1 = 1/4

SLLN ORIGINAL deviating word7 probability factor2 := mul(1/4, 1/2)

SLLN ORIGINAL deviating word7 probability factor2 = 1/8

SLLN ORIGINAL deviation probability word7 := sum(1/8, 1/8)

SLLN ORIGINAL deviation probability word7 = 1/4

source roles = [3, 7, [2, 2, 2], 3/2, 1/2]

derived = [2, 1/2, 是, 1/8, 2, 1/4]

逐步反向核對

• S057 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S056 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviation probability word7，不以小數近似替代。
• S055 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word7 probability factor2，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word7 probability factor1，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word7 probability factor0，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 mean minus mu，不以小數近似替代。
• S051 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 mean，不以小數近似替代。
• S050 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word7 integer sum，不以小數近似替代。
• S049 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S048 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 mean minus mu，不以小數近似替代。
• S047 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 mean，不以小數近似替代。
• S046 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word6 integer sum，不以小數近似替代。
• S045 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S044 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 mean minus mu，不以小數近似替代。
• S043 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 mean，不以小數近似替代。
• S042 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word5 integer sum，不以小數近似替代。
• S041 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S040 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 mean minus mu，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 mean，不以小數近似替代。
• S038 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word4 integer sum，不以小數近似替代。
• S037 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S036 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 mean minus mu，不以小數近似替代。
• S035 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 mean，不以小數近似替代。
• S034 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word3 integer sum，不以小數近似替代。
• S033 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S032 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 mean minus mu，不以小數近似替代。
• S031 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 mean，不以小數近似替代。
• S030 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word2 integer sum，不以小數近似替代。
• S029 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S028 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 mean minus mu，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 mean，不以小數近似替代。
• S026 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word1 integer sum，不以小數近似替代。
• S025 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S024 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviation probability word0，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor2，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor1，不以小數近似替代。
• S021 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL deviating word0 probability factor0，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 mean minus mu，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 mean，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL joint word0 integer sum，不以小數近似替代。
• S017 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S016 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second minus mean squared，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean squared，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second moment sum1，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted square1，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal exact unbounded value square1，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean sum1，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted value1，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL second moment sum0，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted square0，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal exact unbounded value square0，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mean sum0，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL weighted value0，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mass sum1，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 SLLN ORIGINAL common marginal ORIGINAL mass sum0，不以小數近似替代。
• S002 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。
• S001 · premise_and_result_audit — 回查原始資料、操作數、完整範圍與本步前提；有限見證、條件式定理引用與形式證明分開。

結論

(3, 3/2, 1/2, 2, 1/4, fixed_n_deviation_event, 否, not_an_almost_sure_limit_certificate)

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。