概率论问题，随机变量X，Y独立，请问D(XY)=DX.DY吗，请给出证明。

不等于。证明如下DX=EX^2-(EX)^2 DY=EY^2-(EY)^2 EXY=EXEY DXY=E(XY)^2-(EXY)^2=(EX^2)(EY^2)-(EXY)(EXY)=DXDY+EX^2(EY)^2+(EX)^2EY^2-2(EX)^2(EY)^2 =DXDY+(EX)^2(EY^2-(EY)^2)+(EY)^2(EX^2-(EX)^2)=D(X)D(Y)+(E(x))^2D(Y)+E((Y))^2D(x)