Question

若随机变量X与Y相互独立,则D(XY)=DXgDY 判断对错,

Answer 1

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

==[D(X)D(Y)+D(Y)E(X)^2+D(X)E(Y)^2]