第 27297 題：有限變異數IID中央極限定理

原題與已知條件

明示無限IID、共同mu、0<sigma^2<infinity與sigma*sqrt(n)標準化責任。操作=clt-standardized-sum-moments；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 明示無限IID、共同mu、0<sigma^2<infinity與sigma*sqrt(n)標準化責任。操作=clt-standardized-sum-moments；資料={"values":[-1,0],"probabilities":[[1,2],[1,2]],"process_certificate":"infinite_iid","n":5}。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-central-limit-theorem-finite-variance-iid

逐步推導

source roles = [clt-standardized-sum-moments]

derived = [[n, sum_distribution, total_probability, sum_mean, sum_variance, n_times_mean, n_times_variance, standardized_mean, standardized_variance, standardization_description, finite_scope]]

source roles = [infinite_iid]

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

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

CLT ORIGINAL common marginal ORIGINAL law mass sum0 = 1/2

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

CLT ORIGINAL common marginal ORIGINAL law mass sum1 = 1

source roles = [CLT ORIGINAL common marginal, [-1, 0], [[1, 2], [1, 2]]]

derived = [[[-1, 1/2], [0, 1/2]], 1]

CLT ORIGINAL common marginal ORIGINAL value times probability0 := mul(-1, 1/2)

CLT ORIGINAL common marginal ORIGINAL value times probability0 = -1/2

CLT ORIGINAL common marginal ORIGINAL ascending mean sum0 := sum(0, -1/2)

CLT ORIGINAL common marginal ORIGINAL ascending mean sum0 = -1/2

CLT ORIGINAL common marginal exact value square0 := mul(-1, -1)

CLT ORIGINAL common marginal exact value square0 = 1

CLT ORIGINAL common marginal ORIGINAL square times probability0 := mul(1, 1/2)

CLT ORIGINAL common marginal ORIGINAL square times probability0 = 1/2

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

CLT ORIGINAL common marginal ORIGINAL ascending second moment sum0 = 1/2

CLT ORIGINAL common marginal ORIGINAL value times probability1 := mul(0, 1/2)

CLT ORIGINAL common marginal ORIGINAL value times probability1 = 0

CLT ORIGINAL common marginal ORIGINAL ascending mean sum1 := sum(-1/2, 0)

CLT ORIGINAL common marginal ORIGINAL ascending mean sum1 = -1/2

CLT ORIGINAL common marginal exact value square1 := mul(0, 0)

CLT ORIGINAL common marginal exact value square1 = 0

CLT ORIGINAL common marginal ORIGINAL square times probability1 := mul(0, 1/2)

CLT ORIGINAL common marginal ORIGINAL square times probability1 = 0

CLT ORIGINAL common marginal ORIGINAL ascending second moment sum1 := sum(1/2, 0)

CLT ORIGINAL common marginal ORIGINAL ascending second moment sum1 = 1/2

CLT ORIGINAL common marginal ORIGINAL mean square := mul(-1/2, -1/2)

CLT ORIGINAL common marginal ORIGINAL mean square = 1/4

CLT ORIGINAL common marginal ORIGINAL second minus mean square := sub(1/2, 1/4)

CLT ORIGINAL common marginal ORIGINAL second minus mean square = 1/4

source roles = [CLT ORIGINAL common marginal, [[-1, 1/2], [0, 1/2]]]

derived = [-1/2, 1/2, 1/4]

CLT joint ORIGINAL word0 sum := sum(-1, -1, -1, -1, -1)

CLT joint ORIGINAL word0 sum = -5

CLT joint ORIGINAL word0 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word0 probability factor0 = 1/2

CLT joint ORIGINAL word0 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word0 probability factor1 = 1/4

CLT joint ORIGINAL word0 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word0 probability factor2 = 1/8

CLT joint ORIGINAL word0 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word0 probability factor3 = 1/16

CLT joint ORIGINAL word0 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word0 probability factor4 = 1/32

CLT joint ORIGINAL sum-5 bucket word0 := sum(0, 1/32)

CLT joint ORIGINAL sum-5 bucket word0 = 1/32

source roles = [5, 0, [-1, -1, -1, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-5, 1/32, 0, 1/32]

CLT joint ORIGINAL word1 sum := sum(-1, -1, -1, -1, 0)

CLT joint ORIGINAL word1 sum = -4

CLT joint ORIGINAL word1 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word1 probability factor0 = 1/2

CLT joint ORIGINAL word1 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word1 probability factor1 = 1/4

CLT joint ORIGINAL word1 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word1 probability factor2 = 1/8

CLT joint ORIGINAL word1 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word1 probability factor3 = 1/16

CLT joint ORIGINAL word1 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word1 probability factor4 = 1/32

CLT joint ORIGINAL sum-4 bucket word1 := sum(0, 1/32)

CLT joint ORIGINAL sum-4 bucket word1 = 1/32

source roles = [5, 1, [-1, -1, -1, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-4, 1/32, 0, 1/32]

CLT joint ORIGINAL word2 sum := sum(-1, -1, -1, 0, -1)

CLT joint ORIGINAL word2 sum = -4

CLT joint ORIGINAL word2 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word2 probability factor0 = 1/2

CLT joint ORIGINAL word2 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word2 probability factor1 = 1/4

CLT joint ORIGINAL word2 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word2 probability factor2 = 1/8

CLT joint ORIGINAL word2 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word2 probability factor3 = 1/16

CLT joint ORIGINAL word2 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word2 probability factor4 = 1/32

CLT joint ORIGINAL sum-4 bucket word2 := sum(1/32, 1/32)

CLT joint ORIGINAL sum-4 bucket word2 = 1/16

source roles = [5, 2, [-1, -1, -1, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-4, 1/32, 1/32, 1/16]

CLT joint ORIGINAL word3 sum := sum(-1, -1, -1, 0, 0)

CLT joint ORIGINAL word3 sum = -3

CLT joint ORIGINAL word3 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word3 probability factor0 = 1/2

CLT joint ORIGINAL word3 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word3 probability factor1 = 1/4

CLT joint ORIGINAL word3 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word3 probability factor2 = 1/8

CLT joint ORIGINAL word3 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word3 probability factor3 = 1/16

CLT joint ORIGINAL word3 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word3 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word3 := sum(0, 1/32)

CLT joint ORIGINAL sum-3 bucket word3 = 1/32

source roles = [5, 3, [-1, -1, -1, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 0, 1/32]

CLT joint ORIGINAL word4 sum := sum(-1, -1, 0, -1, -1)

CLT joint ORIGINAL word4 sum = -4

CLT joint ORIGINAL word4 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word4 probability factor0 = 1/2

CLT joint ORIGINAL word4 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word4 probability factor1 = 1/4

CLT joint ORIGINAL word4 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word4 probability factor2 = 1/8

CLT joint ORIGINAL word4 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word4 probability factor3 = 1/16

CLT joint ORIGINAL word4 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word4 probability factor4 = 1/32

CLT joint ORIGINAL sum-4 bucket word4 := sum(1/16, 1/32)

CLT joint ORIGINAL sum-4 bucket word4 = 3/32

source roles = [5, 4, [-1, -1, 0, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-4, 1/32, 1/16, 3/32]

CLT joint ORIGINAL word5 sum := sum(-1, -1, 0, -1, 0)

CLT joint ORIGINAL word5 sum = -3

CLT joint ORIGINAL word5 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word5 probability factor0 = 1/2

CLT joint ORIGINAL word5 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word5 probability factor1 = 1/4

CLT joint ORIGINAL word5 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word5 probability factor2 = 1/8

CLT joint ORIGINAL word5 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word5 probability factor3 = 1/16

CLT joint ORIGINAL word5 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word5 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word5 := sum(1/32, 1/32)

CLT joint ORIGINAL sum-3 bucket word5 = 1/16

source roles = [5, 5, [-1, -1, 0, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 1/32, 1/16]

CLT joint ORIGINAL word6 sum := sum(-1, -1, 0, 0, -1)

CLT joint ORIGINAL word6 sum = -3

CLT joint ORIGINAL word6 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word6 probability factor0 = 1/2

CLT joint ORIGINAL word6 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word6 probability factor1 = 1/4

CLT joint ORIGINAL word6 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word6 probability factor2 = 1/8

CLT joint ORIGINAL word6 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word6 probability factor3 = 1/16

CLT joint ORIGINAL word6 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word6 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word6 := sum(1/16, 1/32)

CLT joint ORIGINAL sum-3 bucket word6 = 3/32

source roles = [5, 6, [-1, -1, 0, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 1/16, 3/32]

CLT joint ORIGINAL word7 sum := sum(-1, -1, 0, 0, 0)

CLT joint ORIGINAL word7 sum = -2

CLT joint ORIGINAL word7 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word7 probability factor0 = 1/2

CLT joint ORIGINAL word7 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word7 probability factor1 = 1/4

CLT joint ORIGINAL word7 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word7 probability factor2 = 1/8

CLT joint ORIGINAL word7 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word7 probability factor3 = 1/16

CLT joint ORIGINAL word7 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word7 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word7 := sum(0, 1/32)

CLT joint ORIGINAL sum-2 bucket word7 = 1/32

source roles = [5, 7, [-1, -1, 0, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 0, 1/32]

CLT joint ORIGINAL word8 sum := sum(-1, 0, -1, -1, -1)

CLT joint ORIGINAL word8 sum = -4

CLT joint ORIGINAL word8 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word8 probability factor0 = 1/2

CLT joint ORIGINAL word8 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word8 probability factor1 = 1/4

CLT joint ORIGINAL word8 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word8 probability factor2 = 1/8

CLT joint ORIGINAL word8 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word8 probability factor3 = 1/16

CLT joint ORIGINAL word8 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word8 probability factor4 = 1/32

CLT joint ORIGINAL sum-4 bucket word8 := sum(3/32, 1/32)

CLT joint ORIGINAL sum-4 bucket word8 = 1/8

source roles = [5, 8, [-1, 0, -1, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-4, 1/32, 3/32, 1/8]

CLT joint ORIGINAL word9 sum := sum(-1, 0, -1, -1, 0)

CLT joint ORIGINAL word9 sum = -3

CLT joint ORIGINAL word9 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word9 probability factor0 = 1/2

CLT joint ORIGINAL word9 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word9 probability factor1 = 1/4

CLT joint ORIGINAL word9 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word9 probability factor2 = 1/8

CLT joint ORIGINAL word9 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word9 probability factor3 = 1/16

CLT joint ORIGINAL word9 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word9 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word9 := sum(3/32, 1/32)

CLT joint ORIGINAL sum-3 bucket word9 = 1/8

source roles = [5, 9, [-1, 0, -1, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 3/32, 1/8]

CLT joint ORIGINAL word10 sum := sum(-1, 0, -1, 0, -1)

CLT joint ORIGINAL word10 sum = -3

CLT joint ORIGINAL word10 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word10 probability factor0 = 1/2

CLT joint ORIGINAL word10 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word10 probability factor1 = 1/4

CLT joint ORIGINAL word10 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word10 probability factor2 = 1/8

CLT joint ORIGINAL word10 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word10 probability factor3 = 1/16

CLT joint ORIGINAL word10 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word10 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word10 := sum(1/8, 1/32)

CLT joint ORIGINAL sum-3 bucket word10 = 5/32

source roles = [5, 10, [-1, 0, -1, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 1/8, 5/32]

CLT joint ORIGINAL word11 sum := sum(-1, 0, -1, 0, 0)

CLT joint ORIGINAL word11 sum = -2

CLT joint ORIGINAL word11 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word11 probability factor0 = 1/2

CLT joint ORIGINAL word11 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word11 probability factor1 = 1/4

CLT joint ORIGINAL word11 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word11 probability factor2 = 1/8

CLT joint ORIGINAL word11 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word11 probability factor3 = 1/16

CLT joint ORIGINAL word11 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word11 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word11 := sum(1/32, 1/32)

CLT joint ORIGINAL sum-2 bucket word11 = 1/16

source roles = [5, 11, [-1, 0, -1, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 1/32, 1/16]

CLT joint ORIGINAL word12 sum := sum(-1, 0, 0, -1, -1)

CLT joint ORIGINAL word12 sum = -3

CLT joint ORIGINAL word12 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word12 probability factor0 = 1/2

CLT joint ORIGINAL word12 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word12 probability factor1 = 1/4

CLT joint ORIGINAL word12 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word12 probability factor2 = 1/8

CLT joint ORIGINAL word12 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word12 probability factor3 = 1/16

CLT joint ORIGINAL word12 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word12 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word12 := sum(5/32, 1/32)

CLT joint ORIGINAL sum-3 bucket word12 = 3/16

source roles = [5, 12, [-1, 0, 0, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 5/32, 3/16]

CLT joint ORIGINAL word13 sum := sum(-1, 0, 0, -1, 0)

CLT joint ORIGINAL word13 sum = -2

CLT joint ORIGINAL word13 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word13 probability factor0 = 1/2

CLT joint ORIGINAL word13 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word13 probability factor1 = 1/4

CLT joint ORIGINAL word13 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word13 probability factor2 = 1/8

CLT joint ORIGINAL word13 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word13 probability factor3 = 1/16

CLT joint ORIGINAL word13 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word13 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word13 := sum(1/16, 1/32)

CLT joint ORIGINAL sum-2 bucket word13 = 3/32

source roles = [5, 13, [-1, 0, 0, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 1/16, 3/32]

CLT joint ORIGINAL word14 sum := sum(-1, 0, 0, 0, -1)

CLT joint ORIGINAL word14 sum = -2

CLT joint ORIGINAL word14 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word14 probability factor0 = 1/2

CLT joint ORIGINAL word14 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word14 probability factor1 = 1/4

CLT joint ORIGINAL word14 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word14 probability factor2 = 1/8

CLT joint ORIGINAL word14 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word14 probability factor3 = 1/16

CLT joint ORIGINAL word14 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word14 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word14 := sum(3/32, 1/32)

CLT joint ORIGINAL sum-2 bucket word14 = 1/8

source roles = [5, 14, [-1, 0, 0, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 3/32, 1/8]

CLT joint ORIGINAL word15 sum := sum(-1, 0, 0, 0, 0)

CLT joint ORIGINAL word15 sum = -1

CLT joint ORIGINAL word15 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word15 probability factor0 = 1/2

CLT joint ORIGINAL word15 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word15 probability factor1 = 1/4

CLT joint ORIGINAL word15 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word15 probability factor2 = 1/8

CLT joint ORIGINAL word15 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word15 probability factor3 = 1/16

CLT joint ORIGINAL word15 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word15 probability factor4 = 1/32

CLT joint ORIGINAL sum-1 bucket word15 := sum(0, 1/32)

CLT joint ORIGINAL sum-1 bucket word15 = 1/32

source roles = [5, 15, [-1, 0, 0, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-1, 1/32, 0, 1/32]

CLT joint ORIGINAL word16 sum := sum(0, -1, -1, -1, -1)

CLT joint ORIGINAL word16 sum = -4

CLT joint ORIGINAL word16 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word16 probability factor0 = 1/2

CLT joint ORIGINAL word16 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word16 probability factor1 = 1/4

CLT joint ORIGINAL word16 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word16 probability factor2 = 1/8

CLT joint ORIGINAL word16 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word16 probability factor3 = 1/16

CLT joint ORIGINAL word16 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word16 probability factor4 = 1/32

CLT joint ORIGINAL sum-4 bucket word16 := sum(1/8, 1/32)

CLT joint ORIGINAL sum-4 bucket word16 = 5/32

source roles = [5, 16, [0, -1, -1, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-4, 1/32, 1/8, 5/32]

CLT joint ORIGINAL word17 sum := sum(0, -1, -1, -1, 0)

CLT joint ORIGINAL word17 sum = -3

CLT joint ORIGINAL word17 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word17 probability factor0 = 1/2

CLT joint ORIGINAL word17 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word17 probability factor1 = 1/4

CLT joint ORIGINAL word17 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word17 probability factor2 = 1/8

CLT joint ORIGINAL word17 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word17 probability factor3 = 1/16

CLT joint ORIGINAL word17 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word17 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word17 := sum(3/16, 1/32)

CLT joint ORIGINAL sum-3 bucket word17 = 7/32

source roles = [5, 17, [0, -1, -1, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 3/16, 7/32]

CLT joint ORIGINAL word18 sum := sum(0, -1, -1, 0, -1)

CLT joint ORIGINAL word18 sum = -3

CLT joint ORIGINAL word18 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word18 probability factor0 = 1/2

CLT joint ORIGINAL word18 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word18 probability factor1 = 1/4

CLT joint ORIGINAL word18 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word18 probability factor2 = 1/8

CLT joint ORIGINAL word18 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word18 probability factor3 = 1/16

CLT joint ORIGINAL word18 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word18 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word18 := sum(7/32, 1/32)

CLT joint ORIGINAL sum-3 bucket word18 = 1/4

source roles = [5, 18, [0, -1, -1, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 7/32, 1/4]

CLT joint ORIGINAL word19 sum := sum(0, -1, -1, 0, 0)

CLT joint ORIGINAL word19 sum = -2

CLT joint ORIGINAL word19 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word19 probability factor0 = 1/2

CLT joint ORIGINAL word19 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word19 probability factor1 = 1/4

CLT joint ORIGINAL word19 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word19 probability factor2 = 1/8

CLT joint ORIGINAL word19 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word19 probability factor3 = 1/16

CLT joint ORIGINAL word19 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word19 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word19 := sum(1/8, 1/32)

CLT joint ORIGINAL sum-2 bucket word19 = 5/32

source roles = [5, 19, [0, -1, -1, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 1/8, 5/32]

CLT joint ORIGINAL word20 sum := sum(0, -1, 0, -1, -1)

CLT joint ORIGINAL word20 sum = -3

CLT joint ORIGINAL word20 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word20 probability factor0 = 1/2

CLT joint ORIGINAL word20 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word20 probability factor1 = 1/4

CLT joint ORIGINAL word20 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word20 probability factor2 = 1/8

CLT joint ORIGINAL word20 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word20 probability factor3 = 1/16

CLT joint ORIGINAL word20 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word20 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word20 := sum(1/4, 1/32)

CLT joint ORIGINAL sum-3 bucket word20 = 9/32

source roles = [5, 20, [0, -1, 0, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 1/4, 9/32]

CLT joint ORIGINAL word21 sum := sum(0, -1, 0, -1, 0)

CLT joint ORIGINAL word21 sum = -2

CLT joint ORIGINAL word21 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word21 probability factor0 = 1/2

CLT joint ORIGINAL word21 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word21 probability factor1 = 1/4

CLT joint ORIGINAL word21 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word21 probability factor2 = 1/8

CLT joint ORIGINAL word21 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word21 probability factor3 = 1/16

CLT joint ORIGINAL word21 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word21 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word21 := sum(5/32, 1/32)

CLT joint ORIGINAL sum-2 bucket word21 = 3/16

source roles = [5, 21, [0, -1, 0, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 5/32, 3/16]

CLT joint ORIGINAL word22 sum := sum(0, -1, 0, 0, -1)

CLT joint ORIGINAL word22 sum = -2

CLT joint ORIGINAL word22 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word22 probability factor0 = 1/2

CLT joint ORIGINAL word22 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word22 probability factor1 = 1/4

CLT joint ORIGINAL word22 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word22 probability factor2 = 1/8

CLT joint ORIGINAL word22 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word22 probability factor3 = 1/16

CLT joint ORIGINAL word22 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word22 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word22 := sum(3/16, 1/32)

CLT joint ORIGINAL sum-2 bucket word22 = 7/32

source roles = [5, 22, [0, -1, 0, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 3/16, 7/32]

CLT joint ORIGINAL word23 sum := sum(0, -1, 0, 0, 0)

CLT joint ORIGINAL word23 sum = -1

CLT joint ORIGINAL word23 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word23 probability factor0 = 1/2

CLT joint ORIGINAL word23 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word23 probability factor1 = 1/4

CLT joint ORIGINAL word23 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word23 probability factor2 = 1/8

CLT joint ORIGINAL word23 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word23 probability factor3 = 1/16

CLT joint ORIGINAL word23 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word23 probability factor4 = 1/32

CLT joint ORIGINAL sum-1 bucket word23 := sum(1/32, 1/32)

CLT joint ORIGINAL sum-1 bucket word23 = 1/16

source roles = [5, 23, [0, -1, 0, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-1, 1/32, 1/32, 1/16]

CLT joint ORIGINAL word24 sum := sum(0, 0, -1, -1, -1)

CLT joint ORIGINAL word24 sum = -3

CLT joint ORIGINAL word24 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word24 probability factor0 = 1/2

CLT joint ORIGINAL word24 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word24 probability factor1 = 1/4

CLT joint ORIGINAL word24 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word24 probability factor2 = 1/8

CLT joint ORIGINAL word24 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word24 probability factor3 = 1/16

CLT joint ORIGINAL word24 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word24 probability factor4 = 1/32

CLT joint ORIGINAL sum-3 bucket word24 := sum(9/32, 1/32)

CLT joint ORIGINAL sum-3 bucket word24 = 5/16

source roles = [5, 24, [0, 0, -1, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-3, 1/32, 9/32, 5/16]

CLT joint ORIGINAL word25 sum := sum(0, 0, -1, -1, 0)

CLT joint ORIGINAL word25 sum = -2

CLT joint ORIGINAL word25 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word25 probability factor0 = 1/2

CLT joint ORIGINAL word25 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word25 probability factor1 = 1/4

CLT joint ORIGINAL word25 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word25 probability factor2 = 1/8

CLT joint ORIGINAL word25 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word25 probability factor3 = 1/16

CLT joint ORIGINAL word25 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word25 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word25 := sum(7/32, 1/32)

CLT joint ORIGINAL sum-2 bucket word25 = 1/4

source roles = [5, 25, [0, 0, -1, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 7/32, 1/4]

CLT joint ORIGINAL word26 sum := sum(0, 0, -1, 0, -1)

CLT joint ORIGINAL word26 sum = -2

CLT joint ORIGINAL word26 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word26 probability factor0 = 1/2

CLT joint ORIGINAL word26 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word26 probability factor1 = 1/4

CLT joint ORIGINAL word26 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word26 probability factor2 = 1/8

CLT joint ORIGINAL word26 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word26 probability factor3 = 1/16

CLT joint ORIGINAL word26 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word26 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word26 := sum(1/4, 1/32)

CLT joint ORIGINAL sum-2 bucket word26 = 9/32

source roles = [5, 26, [0, 0, -1, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 1/4, 9/32]

CLT joint ORIGINAL word27 sum := sum(0, 0, -1, 0, 0)

CLT joint ORIGINAL word27 sum = -1

CLT joint ORIGINAL word27 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word27 probability factor0 = 1/2

CLT joint ORIGINAL word27 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word27 probability factor1 = 1/4

CLT joint ORIGINAL word27 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word27 probability factor2 = 1/8

CLT joint ORIGINAL word27 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word27 probability factor3 = 1/16

CLT joint ORIGINAL word27 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word27 probability factor4 = 1/32

CLT joint ORIGINAL sum-1 bucket word27 := sum(1/16, 1/32)

CLT joint ORIGINAL sum-1 bucket word27 = 3/32

source roles = [5, 27, [0, 0, -1, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-1, 1/32, 1/16, 3/32]

CLT joint ORIGINAL word28 sum := sum(0, 0, 0, -1, -1)

CLT joint ORIGINAL word28 sum = -2

CLT joint ORIGINAL word28 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word28 probability factor0 = 1/2

CLT joint ORIGINAL word28 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word28 probability factor1 = 1/4

CLT joint ORIGINAL word28 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word28 probability factor2 = 1/8

CLT joint ORIGINAL word28 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word28 probability factor3 = 1/16

CLT joint ORIGINAL word28 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word28 probability factor4 = 1/32

CLT joint ORIGINAL sum-2 bucket word28 := sum(9/32, 1/32)

CLT joint ORIGINAL sum-2 bucket word28 = 5/16

source roles = [5, 28, [0, 0, 0, -1, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-2, 1/32, 9/32, 5/16]

CLT joint ORIGINAL word29 sum := sum(0, 0, 0, -1, 0)

CLT joint ORIGINAL word29 sum = -1

CLT joint ORIGINAL word29 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word29 probability factor0 = 1/2

CLT joint ORIGINAL word29 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word29 probability factor1 = 1/4

CLT joint ORIGINAL word29 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word29 probability factor2 = 1/8

CLT joint ORIGINAL word29 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word29 probability factor3 = 1/16

CLT joint ORIGINAL word29 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word29 probability factor4 = 1/32

CLT joint ORIGINAL sum-1 bucket word29 := sum(3/32, 1/32)

CLT joint ORIGINAL sum-1 bucket word29 = 1/8

source roles = [5, 29, [0, 0, 0, -1, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-1, 1/32, 3/32, 1/8]

CLT joint ORIGINAL word30 sum := sum(0, 0, 0, 0, -1)

CLT joint ORIGINAL word30 sum = -1

CLT joint ORIGINAL word30 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word30 probability factor0 = 1/2

CLT joint ORIGINAL word30 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word30 probability factor1 = 1/4

CLT joint ORIGINAL word30 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word30 probability factor2 = 1/8

CLT joint ORIGINAL word30 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word30 probability factor3 = 1/16

CLT joint ORIGINAL word30 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word30 probability factor4 = 1/32

CLT joint ORIGINAL sum-1 bucket word30 := sum(1/8, 1/32)

CLT joint ORIGINAL sum-1 bucket word30 = 5/32

source roles = [5, 30, [0, 0, 0, 0, -1], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [-1, 1/32, 1/8, 5/32]

CLT joint ORIGINAL word31 sum := sum(0, 0, 0, 0, 0)

CLT joint ORIGINAL word31 sum = 0

CLT joint ORIGINAL word31 probability factor0 := mul(1, 1/2)

CLT joint ORIGINAL word31 probability factor0 = 1/2

CLT joint ORIGINAL word31 probability factor1 := mul(1/2, 1/2)

CLT joint ORIGINAL word31 probability factor1 = 1/4

CLT joint ORIGINAL word31 probability factor2 := mul(1/4, 1/2)

CLT joint ORIGINAL word31 probability factor2 = 1/8

CLT joint ORIGINAL word31 probability factor3 := mul(1/8, 1/2)

CLT joint ORIGINAL word31 probability factor3 = 1/16

CLT joint ORIGINAL word31 probability factor4 := mul(1/16, 1/2)

CLT joint ORIGINAL word31 probability factor4 = 1/32

CLT joint ORIGINAL sum0 bucket word31 := sum(0, 1/32)

CLT joint ORIGINAL sum0 bucket word31 = 1/32

source roles = [5, 31, [0, 0, 0, 0, 0], [1/2, 1/2, 1/2, 1/2, 1/2]]

derived = [0, 1/32, 0, 1/32]

CLT SUM ORIGINAL total distribution mass0 := sum(0, 1/32)

CLT SUM ORIGINAL total distribution mass0 = 1/32

CLT SUM ORIGINAL total distribution mass1 := sum(1/32, 5/32)

CLT SUM ORIGINAL total distribution mass1 = 3/16

CLT SUM ORIGINAL total distribution mass2 := sum(3/16, 5/16)

CLT SUM ORIGINAL total distribution mass2 = 1/2

CLT SUM ORIGINAL total distribution mass3 := sum(1/2, 5/16)

CLT SUM ORIGINAL total distribution mass3 = 13/16

CLT SUM ORIGINAL total distribution mass4 := sum(13/16, 5/32)

CLT SUM ORIGINAL total distribution mass4 = 31/32

CLT SUM ORIGINAL total distribution mass5 := sum(31/32, 1/32)

CLT SUM ORIGINAL total distribution mass5 = 1

CLT SUM ORIGINAL value times probability0 := mul(-5, 1/32)

CLT SUM ORIGINAL value times probability0 = -5/32

CLT SUM ORIGINAL ascending mean sum0 := sum(0, -5/32)

CLT SUM ORIGINAL ascending mean sum0 = -5/32

CLT SUM exact value square0 := mul(-5, -5)

CLT SUM exact value square0 = 25

CLT SUM ORIGINAL square times probability0 := mul(25, 1/32)

CLT SUM ORIGINAL square times probability0 = 25/32

CLT SUM ORIGINAL ascending second moment sum0 := sum(0, 25/32)

CLT SUM ORIGINAL ascending second moment sum0 = 25/32

CLT SUM ORIGINAL value times probability1 := mul(-4, 5/32)

CLT SUM ORIGINAL value times probability1 = -5/8

CLT SUM ORIGINAL ascending mean sum1 := sum(-5/32, -5/8)

CLT SUM ORIGINAL ascending mean sum1 = -25/32

CLT SUM exact value square1 := mul(-4, -4)

CLT SUM exact value square1 = 16

CLT SUM ORIGINAL square times probability1 := mul(16, 5/32)

CLT SUM ORIGINAL square times probability1 = 5/2

CLT SUM ORIGINAL ascending second moment sum1 := sum(25/32, 5/2)

CLT SUM ORIGINAL ascending second moment sum1 = 105/32

CLT SUM ORIGINAL value times probability2 := mul(-3, 5/16)

CLT SUM ORIGINAL value times probability2 = -15/16

CLT SUM ORIGINAL ascending mean sum2 := sum(-25/32, -15/16)

CLT SUM ORIGINAL ascending mean sum2 = -55/32

CLT SUM exact value square2 := mul(-3, -3)

CLT SUM exact value square2 = 9

CLT SUM ORIGINAL square times probability2 := mul(9, 5/16)

CLT SUM ORIGINAL square times probability2 = 45/16

CLT SUM ORIGINAL ascending second moment sum2 := sum(105/32, 45/16)

CLT SUM ORIGINAL ascending second moment sum2 = 195/32

CLT SUM ORIGINAL value times probability3 := mul(-2, 5/16)

CLT SUM ORIGINAL value times probability3 = -5/8

CLT SUM ORIGINAL ascending mean sum3 := sum(-55/32, -5/8)

CLT SUM ORIGINAL ascending mean sum3 = -75/32

CLT SUM exact value square3 := mul(-2, -2)

CLT SUM exact value square3 = 4

CLT SUM ORIGINAL square times probability3 := mul(4, 5/16)

CLT SUM ORIGINAL square times probability3 = 5/4

CLT SUM ORIGINAL ascending second moment sum3 := sum(195/32, 5/4)

CLT SUM ORIGINAL ascending second moment sum3 = 235/32

CLT SUM ORIGINAL value times probability4 := mul(-1, 5/32)

CLT SUM ORIGINAL value times probability4 = -5/32

CLT SUM ORIGINAL ascending mean sum4 := sum(-75/32, -5/32)

CLT SUM ORIGINAL ascending mean sum4 = -5/2

CLT SUM exact value square4 := mul(-1, -1)

CLT SUM exact value square4 = 1

CLT SUM ORIGINAL square times probability4 := mul(1, 5/32)

CLT SUM ORIGINAL square times probability4 = 5/32

CLT SUM ORIGINAL ascending second moment sum4 := sum(235/32, 5/32)

CLT SUM ORIGINAL ascending second moment sum4 = 15/2

CLT SUM ORIGINAL value times probability5 := mul(0, 1/32)

CLT SUM ORIGINAL value times probability5 = 0

CLT SUM ORIGINAL ascending mean sum5 := sum(-5/2, 0)

CLT SUM ORIGINAL ascending mean sum5 = -5/2

CLT SUM exact value square5 := mul(0, 0)

CLT SUM exact value square5 = 0

CLT SUM ORIGINAL square times probability5 := mul(0, 1/32)

CLT SUM ORIGINAL square times probability5 = 0

CLT SUM ORIGINAL ascending second moment sum5 := sum(15/2, 0)

CLT SUM ORIGINAL ascending second moment sum5 = 15/2

CLT SUM ORIGINAL mean square := mul(-5/2, -5/2)

CLT SUM ORIGINAL mean square = 25/4

CLT SUM ORIGINAL second minus mean square := sub(15/2, 25/4)

CLT SUM ORIGINAL second minus mean square = 5/4

CLT ORIGINAL n times common mean := mul(5, -1/2)

CLT ORIGINAL n times common mean = -5/2

CLT ORIGINAL n times common variance := mul(5, 1/4)

CLT ORIGINAL n times common variance = 5/4

source roles = [5, -1/2, 1/4, [(-5, 1/32), (-4, 5/32), (-3, 5/16), (-2, 5/16), (-1, 5/32), (0, 1/32)], -5/2, 5/4]

derived = [1, -5/2, 5/4, 0, 1, Z_n=(S_n-n*mu)/(sigma*sqrt(n))]

逐步反向核對

• S315 · 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。
• S314 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL n times common variance，不以小數近似替代。
• S313 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL n times common mean，不以小數近似替代。
• S312 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL second minus mean square，不以小數近似替代。
• S311 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL mean square，不以小數近似替代。
• S310 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum5，不以小數近似替代。
• S309 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability5，不以小數近似替代。
• S308 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square5，不以小數近似替代。
• S307 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum5，不以小數近似替代。
• S306 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability5，不以小數近似替代。
• S305 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum4，不以小數近似替代。
• S304 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability4，不以小數近似替代。
• S303 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square4，不以小數近似替代。
• S302 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum4，不以小數近似替代。
• S301 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability4，不以小數近似替代。
• S300 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum3，不以小數近似替代。
• S299 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability3，不以小數近似替代。
• S298 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square3，不以小數近似替代。
• S297 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum3，不以小數近似替代。
• S296 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability3，不以小數近似替代。
• S295 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum2，不以小數近似替代。
• S294 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability2，不以小數近似替代。
• S293 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square2，不以小數近似替代。
• S292 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum2，不以小數近似替代。
• S291 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability2，不以小數近似替代。
• S290 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum1，不以小數近似替代。
• S289 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability1，不以小數近似替代。
• S288 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square1，不以小數近似替代。
• S287 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum1，不以小數近似替代。
• S286 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability1，不以小數近似替代。
• S285 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending second moment sum0，不以小數近似替代。
• S284 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL square times probability0，不以小數近似替代。
• S283 · premise_and_result_audit — 以精確有理數重算 CLT SUM exact value square0，不以小數近似替代。
• S282 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL ascending mean sum0，不以小數近似替代。
• S281 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL value times probability0，不以小數近似替代。
• S280 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass5，不以小數近似替代。
• S279 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass4，不以小數近似替代。
• S278 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass3，不以小數近似替代。
• S277 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass2，不以小數近似替代。
• S276 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass1，不以小數近似替代。
• S275 · premise_and_result_audit — 以精確有理數重算 CLT SUM ORIGINAL total distribution mass0，不以小數近似替代。
• S274 · 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。
• S273 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum0 bucket word31，不以小數近似替代。
• S272 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 probability factor4，不以小數近似替代。
• S271 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 probability factor3，不以小數近似替代。
• S270 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 probability factor2，不以小數近似替代。
• S269 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 probability factor1，不以小數近似替代。
• S268 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 probability factor0，不以小數近似替代。
• S267 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word31 sum，不以小數近似替代。
• S266 · 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。
• S265 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-1 bucket word30，不以小數近似替代。
• S264 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 probability factor4，不以小數近似替代。
• S263 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 probability factor3，不以小數近似替代。
• S262 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 probability factor2，不以小數近似替代。
• S261 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 probability factor1，不以小數近似替代。
• S260 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 probability factor0，不以小數近似替代。
• S259 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word30 sum，不以小數近似替代。
• S258 · 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。
• S257 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-1 bucket word29，不以小數近似替代。
• S256 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 probability factor4，不以小數近似替代。
• S255 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 probability factor3，不以小數近似替代。
• S254 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 probability factor2，不以小數近似替代。
• S253 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 probability factor1，不以小數近似替代。
• S252 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 probability factor0，不以小數近似替代。
• S251 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word29 sum，不以小數近似替代。
• S250 · 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。
• S249 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word28，不以小數近似替代。
• S248 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 probability factor4，不以小數近似替代。
• S247 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 probability factor3，不以小數近似替代。
• S246 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 probability factor2，不以小數近似替代。
• S245 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 probability factor1，不以小數近似替代。
• S244 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 probability factor0，不以小數近似替代。
• S243 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word28 sum，不以小數近似替代。
• S242 · 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。
• S241 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-1 bucket word27，不以小數近似替代。
• S240 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 probability factor4，不以小數近似替代。
• S239 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 probability factor3，不以小數近似替代。
• S238 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 probability factor2，不以小數近似替代。
• S237 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 probability factor1，不以小數近似替代。
• S236 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 probability factor0，不以小數近似替代。
• S235 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word27 sum，不以小數近似替代。
• S234 · 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。
• S233 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word26，不以小數近似替代。
• S232 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 probability factor4，不以小數近似替代。
• S231 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 probability factor3，不以小數近似替代。
• S230 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 probability factor2，不以小數近似替代。
• S229 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 probability factor1，不以小數近似替代。
• S228 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 probability factor0，不以小數近似替代。
• S227 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word26 sum，不以小數近似替代。
• S226 · 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。
• S225 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word25，不以小數近似替代。
• S224 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 probability factor4，不以小數近似替代。
• S223 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 probability factor3，不以小數近似替代。
• S222 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 probability factor2，不以小數近似替代。
• S221 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 probability factor1，不以小數近似替代。
• S220 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 probability factor0，不以小數近似替代。
• S219 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word25 sum，不以小數近似替代。
• S218 · 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。
• S217 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word24，不以小數近似替代。
• S216 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 probability factor4，不以小數近似替代。
• S215 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 probability factor3，不以小數近似替代。
• S214 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 probability factor2，不以小數近似替代。
• S213 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 probability factor1，不以小數近似替代。
• S212 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 probability factor0，不以小數近似替代。
• S211 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word24 sum，不以小數近似替代。
• S210 · 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。
• S209 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-1 bucket word23，不以小數近似替代。
• S208 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 probability factor4，不以小數近似替代。
• S207 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 probability factor3，不以小數近似替代。
• S206 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 probability factor2，不以小數近似替代。
• S205 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 probability factor1，不以小數近似替代。
• S204 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 probability factor0，不以小數近似替代。
• S203 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word23 sum，不以小數近似替代。
• S202 · 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。
• S201 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word22，不以小數近似替代。
• S200 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 probability factor4，不以小數近似替代。
• S199 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 probability factor3，不以小數近似替代。
• S198 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 probability factor2，不以小數近似替代。
• S197 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 probability factor1，不以小數近似替代。
• S196 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 probability factor0，不以小數近似替代。
• S195 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word22 sum，不以小數近似替代。
• S194 · 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。
• S193 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word21，不以小數近似替代。
• S192 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 probability factor4，不以小數近似替代。
• S191 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 probability factor3，不以小數近似替代。
• S190 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 probability factor2，不以小數近似替代。
• S189 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 probability factor1，不以小數近似替代。
• S188 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 probability factor0，不以小數近似替代。
• S187 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word21 sum，不以小數近似替代。
• S186 · 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。
• S185 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word20，不以小數近似替代。
• S184 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 probability factor4，不以小數近似替代。
• S183 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 probability factor3，不以小數近似替代。
• S182 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 probability factor2，不以小數近似替代。
• S181 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 probability factor1，不以小數近似替代。
• S180 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 probability factor0，不以小數近似替代。
• S179 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word20 sum，不以小數近似替代。
• S178 · 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。
• S177 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word19，不以小數近似替代。
• S176 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 probability factor4，不以小數近似替代。
• S175 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 probability factor3，不以小數近似替代。
• S174 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 probability factor2，不以小數近似替代。
• S173 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 probability factor1，不以小數近似替代。
• S172 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 probability factor0，不以小數近似替代。
• S171 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word19 sum，不以小數近似替代。
• S170 · 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。
• S169 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word18，不以小數近似替代。
• S168 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 probability factor4，不以小數近似替代。
• S167 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 probability factor3，不以小數近似替代。
• S166 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 probability factor2，不以小數近似替代。
• S165 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 probability factor1，不以小數近似替代。
• S164 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 probability factor0，不以小數近似替代。
• S163 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word18 sum，不以小數近似替代。
• S162 · 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。
• S161 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word17，不以小數近似替代。
• S160 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 probability factor4，不以小數近似替代。
• S159 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 probability factor3，不以小數近似替代。
• S158 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 probability factor2，不以小數近似替代。
• S157 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 probability factor1，不以小數近似替代。
• S156 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 probability factor0，不以小數近似替代。
• S155 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word17 sum，不以小數近似替代。
• S154 · 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。
• S153 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-4 bucket word16，不以小數近似替代。
• S152 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 probability factor4，不以小數近似替代。
• S151 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 probability factor3，不以小數近似替代。
• S150 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 probability factor2，不以小數近似替代。
• S149 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 probability factor1，不以小數近似替代。
• S148 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 probability factor0，不以小數近似替代。
• S147 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word16 sum，不以小數近似替代。
• S146 · 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。
• S145 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-1 bucket word15，不以小數近似替代。
• S144 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 probability factor4，不以小數近似替代。
• S143 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 probability factor3，不以小數近似替代。
• S142 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 probability factor2，不以小數近似替代。
• S141 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 probability factor1，不以小數近似替代。
• S140 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 probability factor0，不以小數近似替代。
• S139 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word15 sum，不以小數近似替代。
• S138 · 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。
• S137 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word14，不以小數近似替代。
• S136 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 probability factor4，不以小數近似替代。
• S135 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 probability factor3，不以小數近似替代。
• S134 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 probability factor2，不以小數近似替代。
• S133 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 probability factor1，不以小數近似替代。
• S132 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 probability factor0，不以小數近似替代。
• S131 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word14 sum，不以小數近似替代。
• S130 · 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。
• S129 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word13，不以小數近似替代。
• S128 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 probability factor4，不以小數近似替代。
• S127 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 probability factor3，不以小數近似替代。
• S126 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 probability factor2，不以小數近似替代。
• S125 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 probability factor1，不以小數近似替代。
• S124 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 probability factor0，不以小數近似替代。
• S123 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word13 sum，不以小數近似替代。
• S122 · 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。
• S121 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word12，不以小數近似替代。
• S120 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 probability factor4，不以小數近似替代。
• S119 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 probability factor3，不以小數近似替代。
• S118 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 probability factor2，不以小數近似替代。
• S117 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 probability factor1，不以小數近似替代。
• S116 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 probability factor0，不以小數近似替代。
• S115 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word12 sum，不以小數近似替代。
• S114 · 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。
• S113 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word11，不以小數近似替代。
• S112 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 probability factor4，不以小數近似替代。
• S111 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 probability factor3，不以小數近似替代。
• S110 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 probability factor2，不以小數近似替代。
• S109 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 probability factor1，不以小數近似替代。
• S108 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 probability factor0，不以小數近似替代。
• S107 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word11 sum，不以小數近似替代。
• S106 · 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。
• S105 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word10，不以小數近似替代。
• S104 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 probability factor4，不以小數近似替代。
• S103 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 probability factor3，不以小數近似替代。
• S102 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 probability factor2，不以小數近似替代。
• S101 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 probability factor1，不以小數近似替代。
• S100 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 probability factor0，不以小數近似替代。
• S099 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word10 sum，不以小數近似替代。
• S098 · 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。
• S097 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word9，不以小數近似替代。
• S096 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 probability factor4，不以小數近似替代。
• S095 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 probability factor3，不以小數近似替代。
• S094 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 probability factor2，不以小數近似替代。
• S093 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 probability factor1，不以小數近似替代。
• S092 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 probability factor0，不以小數近似替代。
• S091 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word9 sum，不以小數近似替代。
• S090 · 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。
• S089 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-4 bucket word8，不以小數近似替代。
• S088 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 probability factor4，不以小數近似替代。
• S087 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 probability factor3，不以小數近似替代。
• S086 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 probability factor2，不以小數近似替代。
• S085 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 probability factor1，不以小數近似替代。
• S084 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 probability factor0，不以小數近似替代。
• S083 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word8 sum，不以小數近似替代。
• S082 · 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。
• S081 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-2 bucket word7，不以小數近似替代。
• S080 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 probability factor4，不以小數近似替代。
• S079 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 probability factor3，不以小數近似替代。
• S078 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 probability factor2，不以小數近似替代。
• S077 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 probability factor1，不以小數近似替代。
• S076 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 probability factor0，不以小數近似替代。
• S075 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word7 sum，不以小數近似替代。
• S074 · 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。
• S073 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word6，不以小數近似替代。
• S072 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 probability factor4，不以小數近似替代。
• S071 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 probability factor3，不以小數近似替代。
• S070 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 probability factor2，不以小數近似替代。
• S069 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 probability factor1，不以小數近似替代。
• S068 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 probability factor0，不以小數近似替代。
• S067 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word6 sum，不以小數近似替代。
• S066 · 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。
• S065 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word5，不以小數近似替代。
• S064 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 probability factor4，不以小數近似替代。
• S063 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 probability factor3，不以小數近似替代。
• S062 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 probability factor2，不以小數近似替代。
• S061 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 probability factor1，不以小數近似替代。
• S060 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 probability factor0，不以小數近似替代。
• S059 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word5 sum，不以小數近似替代。
• S058 · 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。
• S057 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-4 bucket word4，不以小數近似替代。
• S056 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 probability factor4，不以小數近似替代。
• S055 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 probability factor3，不以小數近似替代。
• S054 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 probability factor2，不以小數近似替代。
• S053 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 probability factor1，不以小數近似替代。
• S052 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 probability factor0，不以小數近似替代。
• S051 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word4 sum，不以小數近似替代。
• S050 · 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。
• S049 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-3 bucket word3，不以小數近似替代。
• S048 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 probability factor4，不以小數近似替代。
• S047 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 probability factor3，不以小數近似替代。
• S046 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 probability factor2，不以小數近似替代。
• S045 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 probability factor1，不以小數近似替代。
• S044 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 probability factor0，不以小數近似替代。
• S043 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word3 sum，不以小數近似替代。
• S042 · 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。
• S041 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-4 bucket word2，不以小數近似替代。
• S040 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 probability factor4，不以小數近似替代。
• S039 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 probability factor3，不以小數近似替代。
• S038 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 probability factor2，不以小數近似替代。
• S037 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 probability factor1，不以小數近似替代。
• S036 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 probability factor0，不以小數近似替代。
• S035 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word2 sum，不以小數近似替代。
• S034 · 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。
• S033 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-4 bucket word1，不以小數近似替代。
• S032 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 probability factor4，不以小數近似替代。
• S031 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 probability factor3，不以小數近似替代。
• S030 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 probability factor2，不以小數近似替代。
• S029 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 probability factor1，不以小數近似替代。
• S028 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 probability factor0，不以小數近似替代。
• S027 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word1 sum，不以小數近似替代。
• S026 · 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。
• S025 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL sum-5 bucket word0，不以小數近似替代。
• S024 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 probability factor4，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 probability factor3，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 probability factor2，不以小數近似替代。
• S021 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 probability factor1，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 probability factor0，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 CLT joint ORIGINAL word0 sum，不以小數近似替代。
• 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 — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL second minus mean square，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL mean square，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL ascending second moment sum1，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL square times probability1，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal exact value square1，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL ascending mean sum1，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL value times probability1，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL ascending second moment sum0，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL square times probability0，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal exact value square0，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL ascending mean sum0，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL value times probability0，不以小數近似替代。
• S005 · 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。
• S004 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL law mass sum1，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 CLT ORIGINAL common marginal ORIGINAL law mass sum0，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

(5, [[-5, 1/32], [-4, 5/32], [-3, 5/16], [-2, 5/16], [-1, 5/32], [0, 1/32]], 1, -5/2, 5/4, -5/2, 5/4, 0, 1, Z_n=(S_n-n*mu)/(sigma*sqrt(n)), complete_joint_law_moments_do_not_prove_distributional_convergence)

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。