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:124 ℃ 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...
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