二维离散型随机变量方差怎样算

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/13 15:19:07

二维离散型随机变量方差怎样算
x/y 1 2
1 0.1 0.3
2 0.4 0.2 求D(X) D(Y) 标准协方差.谢谢

E(X) = ∑ xP(x,y) = 1*0.1 + 1*0.3 + 2*0.4 + 2*0.2 = 1.6
D(X) = E[(X-EX)^2] = ∑ (x-EX)^2 P(x,y)
= (1-1.6)^2*0.1+(1-1.6)^2*0.3+(2-1.6)^2*0.4+(2-1.6)^2*0.2
= 0.6^2*0.4 + 0.4^2*0.6 = 0.24
E(Y) = ∑ yP(x,y) = 1*0.1 + 1*0.4 + 2*0.3 + 2*0.2 = 1.5
D(Y) = E[(Y-EY)^2] = ∑ (y-EY)^2 P(x,y)
= (1-1.5)^2*0.1+(1-1.5)^2*0.4+(2-1.5)^2*0.3+(2-1.5)^2*0.2
= 0.5^2*(0.1+0.4+0.3+0.2) = 0.25
E(XY) = ∑ xyP(x,y) = 1*1*0.1 + 1*2*0.3 + 2*1*0.4 + 2*2*0.2 = 2.3
标准协方差 Cov(X,Y) = E(XY) - E(X)E(Y) = 2.3 - 1.6*1.5 = - 0.1

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