如果随机变量X和Y满足E(XY)=E(X)E(Y),则D(X+Y)-D(X-Y)=?
问题描述:
如果随机变量X和Y满足E(XY)=E(X)E(Y),则D(X+Y)-D(X-Y)=?
答
由题知,
X,Y的协方差cov(x,y)=E(XY)-E(X)E(Y)=0
所以,随机变量X和Y不相关
由于,
D(x+y)=Dx+Dy+2*cov(x,y)
D(x-y)=Dx+Dy-2*cov(x,y)
所以,
D(X+Y)-D(X-Y)=4cov(x,y)=0