D(X+Y)=D(X-Y)=DX+DY-2COV(X,Y) 因為X Y相互獨立,所以COV(X,Y)=0.(方差是要算平方的,裡面無論加減,出來都是正的),所以D(X+Y)=D(X-Y)=DX+DY. 用定義做當然也可以,需要一點耐心而已.(不知學姐是否滿意)

根據方差的定義： D(X-Y) = E{[(X-Y)-(EX-EY)]²} = E{(X-Y)²-2(X-Y)(EX-EY)+(EX-EY)²} = E(X²-2XY+Y²) -2(EX-EY)² + (EX-EY)² = E(X²) -0 + E(Y²) - (EX-EY)² = {E(X²)-(EX)²} + {E(²Y)-(EY)²} + 2EXEY = D(X) + D(Y) + 2EXEY D(X-Y) = D(X)+D(Y) + 2EXEY-------------(1) 當乘積：EXEY 為零時， D(X-Y) = D(X) + D(Y)---------------------(2) 請再仔細推導一下！