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3 1.3,, ( ) ( n),, ( ). A, A m, A P (A) = m n = A Ω : A A.,. Previous Next First Last Back Forward 2

4 I n 1 I II n 2 I II n 1 n 2 I n 1 II n 2 I II n 1 + n 2 n, r n r n r n(n 1) (n r + 1) = P r n. n, r ( ) n n(n 1) (n r + 1) n! = = r r! r!(n r)! Previous Next First Last Back Forward 3

5 n, r ( ) ( ) n + r 1 r,.,,? :,. : C 2 4 = 6.?, 3 : C 2 4 /2 = 3 Previous Next First Last Back Forward 4

6 ,,,. 6 3, 2, 3,. 1, C6 2 ; 2, C4 2 ; 3. : C6 2 C4 2 = 6! 4! 4! 2! 2! 2! = 6! 2! 2! 2! = 90. Previous Next First Last Back Forward 5

7 7 3,, 3, 2,. :.. 3,, ( ),, 2! ( ), : 7! 3! 2! 2! 1 2! = 7! 3! (2!) 3., : Previous Next First Last Back Forward 6

8 n, k, n 1, n 2,, n k, n 1 +n 2 + +n k = n,. n! n 1! n 2!... n k! n, k,, n 1, n 2,, n k, n 1 + n n k = n,,. n! n 1! n 2! n k! Previous Next First Last Back Forward 7

9 N M n m (1) (2) : A = { m } (1) Ω = N n, A = ( n m) M m (N M) n m, P (A) = Cm n M m (N M) n m N n = ( n m ) ( M N (2) Ω = C n N, A = C m M C n m N M, P (A) = Cm M C n m N M C n N ) m ( N M ) n m N Previous Next First Last Back Forward 8

10 n, m (m n + 1). A = { }? : (1) Ω = (n + m)!, P (A) = A Ω = n!cm n+1m! (n + m)! A = n!c m n+1m! (2) Ω = (n + m 1)!, A = (n 1)!Cn m m! P (A) = A Ω = (n 1)!Cm n m! (n + m 1)! Previous Next First Last Back Forward 9

11 r 1 n n (1) A={ r } (2) B={ } (3) C={ m } : Ω = n r (1) A = r! (2) B = Cnr! r (3) C = Cr m (n 1) r m,r,n.,. r, n 1, n,., r + n 1, 1 Previous Next First Last Back Forward 10

12 ( ) r, 1 ( ) n 1,, C r r+n 1 = C n 1 r+n 1. ( ) n + r 1 Ω = n 1 (1) A = 1 (2) B = Cn r (3) C = ( ) r m+n 1 1 r m ( ) Previous Next First Last Back Forward 11

13 Maxwell Boltzmann r r r 365 n = 365 B r = 40 P (B) = r = 50, P (B) = 0.03 r = 55 P (B) 0.01 Previous Next First Last Back Forward 12

14 x + y + z = 15, (x, y, z). 15 3, 1, 2, 3 x, y, z., ( ) C = C = = 136; 2 ( ) C = C = = 91. # 2 : Previous Next First Last Back Forward 13

15 n N (1) (2) (3) : A, B, C (1)-(3) Ω = P n N. (1) n N n A = C n N n+1n! (2) B = C n/2 N n+1 n! (3) C = { C n N/22 n n!, nc n 1 (N 1)/2 2n 1 (n 1)! + C n (N 1)/22 n n!, N is even N is odd Previous Next First Last Back Forward 14

16 1.4. Ω 0 < m(ω) < + Ω A, P (A) = m(a) m(ω) Definition A A A " m(ω) Ω. Previous Next First Last Back Forward 15

17 [0, T ] t(t T ) A={ } : x, y A = {(x, y) x y t}, Ω = {(x, y) 0 x, y T } P (A) = m(a) m(ω) = 1 (1 t T )2. Previous Next First Last Back Forward 16

18 a l(l < a) E ={ } ρ 1.1: Previous Next First Last Back Forward 17

19 θ Ω = {(ρ, θ) : 0 ρ a/2, 0 θ π/2}. (ρ, θ) Ω ρ l 2 sinθ. E = {(ρ, θ) Ω : ρ l 2 sinθ} m(ω) = πa π/2 4, m(e) = l 0 2 sinθdθ P (E) = m(e) m(ω) = 2l πa. π 2l ˆpa π Monte-Carlo. Previous Next First Last Back Forward 18

20 A, B, C E={ ABC } (1/4) A, B C, D AB CD (1/3) Previous Next First Last Back Forward 19

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: p Previous Next First Last Back Forward 1 : zwp@ustc.edu.cn Office: 1006 Phone: 63600565 http://staff.ustc.edu.cn/~zwp/ http://fisher.stat.ustc.edu.cn : 7.2......... 1 7.2.1....... 1 7.2.2......... 13 7.2.3................ 18 7.2.4 0-1 p.. 19