Question

设随机变量X,Y相互独立,且E(X)=E(Y)=1,D(X)=2,D(Y)=4,则D(XY)=______

Answer 1

E{[XY-E(XY)]^2}

=E(X^2Y^2)-E(XY)^2

=E(X^2)*E(Y^2)-E(X)^2*E(Y)^2

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

=3*5-1=14