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1. 2. 3. 4. 5. 6. 7. 8. Excel

Excel

chance

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0 1 2 3 4 5 6 7 8 9 10 1 6824 7709 3937 3289 9545 620 3904 5203 6590 8769 2 237 7574 8607 1502 4776 944 4946 1519 4834 2810 3 1336 8960 2192 7132 9267 4262 6070 7664 7690 3873 4 6840 3016 3991 8582 1813 12 3781 8635 286 3932 5 5577 7452 9477 7942 7328 822 7876 6379 9014 6845 6 3495 3500 9497 8688 7764 17 1221 5816 8840 8573 7 5163 5127 5955 7826 982 3563 7783 1575 7738 9146 8 3746 5767 5137 3846 9113 3394 5172 3745 2574 5275 9 596 6736 4273 7665 8229 6933 6510 93 4091 4567 10 6553 4267 4071 3532 593 3874 5368 5295 6303 2629

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1~800

1~800 50

n (X1, X2,..., Xn)

x f 22 1 25 2 28 1 30 1 N = 5

x f(x) 22 1 / 5 = 0.2 25 2 / 5 = 0.4 28 1 / 5 = 0.2 30 1 / 5 = 0.2 f(x) = 1

0.5 f(x) 0.4 0.3 µ = 26 σ 2 = 7.6 0.2 0.1 0 22 25 28 30 x

X f(x) n (X1, X2,..., Xn) X = n / X i n X f] x g i = 1

x1 xn S1 N x1 xn S2 x1 xn S Cn N

x1 xn S1 x 1 = / x n N x1 xn S2 x 2 = / x n x1 xn S Cn N / x x N Cn = n

X x x 1 x 2 x Cn N E X f] x g 1 CN n 1 C n N 1 CN n ] g V] X g

A = 22 B = 25 C = 25 D = 28 E = 30

A = 22 B = 25 C = 25 D = 28 E = 30 (ABC) (ABD) (ABE) (ACD) (ACE) (ADE) (BCD) (BCE) (BDE) (CDE)

A = 22 B = 25 C = 25 D = 28 E = 30 (ABC) (ABD) (ABE) (ACD) (ACE) (ADE) (BCD) (BCE) (BDE) (CDE) X X = X 1 + X 2 + X 3 3

(ABC) = (22, 25, 25) 24 (ABD) = (22, 25, 28) 25 (ABE) = (22, 25, 30) 25.66667 (ACD) = (22, 25, 28) 25 (ACE) = (22, 25, 30) 25.66667 (ADE) = (22, 28, 30) 26.66667 (BCD) = (25, 25, 28) 26 (BCE) = (25, 25, 30) 26.66667 (BDE) = (25, 28, 30) 27.66667 (CDE) = (25, 28, 30) 27.66667 x

x x 2 f] x g x 2 f] x g 24 576 1 / 10 = 0.10 57.6 25 625 2 / 10 = 0.20 125 25.66667 659.7779489 2 / 10 = 0.20 131.7555898 26 676 1 / 10 = 0.10 67.6 26.66667 711.1112889 2 / 10 = 0.20 142.2222578 27.66667 765.4446289 2 / 10 = 0.20 153.0999258 f( x) = 1.00 677.2667733

0.3 f] x g 0.2 0.1 0 24.00 25.00 25.67 26.00 26.67 27.67 x

X X E] X g = n X = n

X X E] X g = n X = n v X 2 = V] X g v 2 v = n v X = n

X X E] X g = n X = n v X 2 = V] X g v 2 v = n v X = n v X 2 = V] X g v 2 N - n = n $ N - 1 v N - n v X = $ n N - 1

X X X ~ N(µ, σ 2 ) n X µ σ 2 / n X = X / n X ~Na v 2 n, n k

X n n n 30

X n n n 30 A B µ µ

A B n = 5 µ µ

A B n = 5 n = 10 µ µ

A B n = 5 n = 10 n = 30 µ µ

A B n = 5 n = 10 n = 30 n = 50 µ µ

1. n 30 X

1. n 30 X 2. (X1, X2,..., Xn)

1. n 30 X 2. (X1, X2,..., Xn) 3.

1. n 30 X 2. (X1, X2,..., Xn) 3. 4.

X (n 30) X ~Na v 2 n, n k X ~Na v 2 n, n k (n < 30) X ~Na v 2 n, n X k

- Excel

p = K N

p = K N W k p = n = n / X i i = 1 n

p = K N W k p = n = n / X i i = 1 n Ea W p k = nw p = p

1. Va W p k = v 2 pq W p = n v p W = n pq

1. Va W p k = v 2 pq W p = n v p W = n pq 2. Va W p k = v 2 pq N - n W p = n $ N - 1 pq N - n vw p = n $ N - 1

E(X) = p, V(X) = pq np > 5, nq > 5 W p ~N b pq p, l W n p~nc pq p, n N - n N - 1 m W p ~ b pq p, l n W p ~ c pq p, n N - n N - 1 m

... K n1 n2 nk

... K

... K n

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18... k (k+1) (k+2)... N

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18... k (k+1) (k+2)... N 6 12 18 n

Excel

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