离散型随机变量的概率分布 ⚫例2:掷二次骰子所得点数之和的概率分布 x 2 3 4 5 6 7 f(x) 1/36 2/36 3/36 4/36 5/36 6/36 x 8 9 10 11 12 f(x) 5/36 4/36 3/36 2/36 1/36 36 21 (7) ( ) 7 2 = = x= F f x 36 6 (7) ( 7) f = P x1 + x2 = = ( ) ( ) 1 2 f x = P x + x = x
离散型随机变量的概率分布 ⚫例2:掷二次骰子所得点数之和的概率分布 x 2 3 4 5 6 7 f(x) 1/36 2/36 3/36 4/36 5/36 6/36 x 8 9 10 11 12 f(x) 5/36 4/36 3/36 2/36 1/36 36 21 (7) ( ) 7 2 = = x= F f x 36 6 (7) ( 7) f = P x1 + x2 = = ( ) ( ) 1 2 f x = P x + x = x
离散型随机变量的概率分布 概率分布图
离散型随机变量的概率分布 概率分布图
离散型随机变量的概率分布 ⚫随机变量的期望(expectation) - 总体平均 数 = ( ) = ( ) i i E X x f x 对于例1: 3.5 (1 2 3 4 5 6) 6 1 6 1 ( ) = = E X = xi = + + + + +
离散型随机变量的概率分布 ⚫随机变量的期望(expectation) - 总体平均 数 = ( ) = ( ) i i E X x f x 对于例1: 3.5 (1 2 3 4 5 6) 6 1 6 1 ( ) = = E X = xi = + + + + +
离散型随机变量的概率分布 ⚫期望的性质 E(a) = a E(X +Y) = E(X ) + E(Y) E(aX ) = aE(X ) (a是常量) E(XY) = E(X )E(Y) 1. 2. 3. 4. (当X和Y彼此独立)
离散型随机变量的概率分布 ⚫期望的性质 E(a) = a E(X +Y) = E(X ) + E(Y) E(aX ) = aE(X ) (a是常量) E(XY) = E(X )E(Y) 1. 2. 3. 4. (当X和Y彼此独立)
离散型随机变量的概率分布 [ ( )] = ( ) ( ) i i E H X H x f x ⚫随机变量的函数的期望 设H(X)是随机变量X的某个函数 ( ) = ( ) 2 2 i i 例: E X x f x 2 H(X) = X 对于例1: 15.167 (1 2 3 4 5 6 ) 6 1 6 1 ( ) 2 2 2 2 2 2 2 2 = E X = xi = + + + + +
离散型随机变量的概率分布 [ ( )] = ( ) ( ) i i E H X H x f x ⚫随机变量的函数的期望 设H(X)是随机变量X的某个函数 ( ) = ( ) 2 2 i i 例: E X x f x 2 H(X) = X 对于例1: 15.167 (1 2 3 4 5 6 ) 6 1 6 1 ( ) 2 2 2 2 2 2 2 2 = E X = xi = + + + + +