Question

方差D(X+Y+5)等于多少,怎样计算呀?

Answer 1

一楼的错了 D(X-Y)=D(X)+D(Y)

D(X+Y+5)=D(X+Y)

=D(X)+D(Y)+2Cov(X,Y)

如果要代数进去 则用D(X+Y),

D(X+Y)=E[(X+Y)]^2-[E(X+Y)]^2(注意中括号位置)

=E(X^2)+E(Y^2)+2E(XY)-(EX)^2-(EY)^2-2EXEY

=D(X)+D(Y)+2[E(XY)-EXEY]