E(XY)=E(X)E(Y),是否能推出D(XY)=D(X)D(Y)希望能有详细点的推导._数学解答

E(XY)=E(X)E(Y),是否能推出D(XY)=D(X)D(Y)
希望能有详细点的推导.

人气：140 ℃　时间：2020-10-01 20:44:22

解答

不能,E(XY)=E(X)E(Y)只能说明x.y独立能够推出D(xy)=D(X)D(Y)+(E(x))^2D(Y)+(E(Y))^2D(x)DX=EX^2-(EX)^2DY=EY^2-(EY)^2EXY=EXEYDXY=E(XY)^2-(EXY)^2=(EX^2)(EY^2)-(EXY)(EXY)=(DX+(EX)^2)(DY+(EY)^2)-(EX)^2(EY)^2 =D...