Question

已知二维随机变量(X,Y)的联合分布律如图片所示,则X与Y的协方差COV(X,Y)=

Answer 1

解：E（Y）=0×（0.3+0.1）+1×（0.2+0.4）=0.6
E（X）=2×（0.3+0.2）+3×（0.1+0.4）=2.5
E（XY）=2*0*0.3 + 3*0*0.1 + 2*1*0.2+3*1*0.4=1.6
则cov（X,Y)=E（XY）-E（x）E（Y）=1.6-2.5*0.6=0.1

Answer 2

解：E（Y）=0×（0.3+0.1）+1×（0.2+0.4）=0.6
E（X）=2×（0.3+0.2）+3×（0.1+0.4）=2.5
E（XY）=2*0*0.3 + 3*0*0.1 + 2*1*0.2+3*1*0.4=1.6
则cov（X,Y)=E（XY）-E（x）E（Y）=1.6-2.5*0.6=0.1