Question

随机变量X,Y,期望均为0,方差均为1,相关系数为r.证明E[max{X^2,Y^2}]小于等于1+（1-r^2)^(1

Answer 1

=Cov(X,Y)/(D(X)D(Y))*0.5

Cov(X,Y)=E(XY)-E(X)E(Y)=E(XY)

得r=E(XY)

设X〉Y

则E(X^2)^2+E(XY)^2