若x与y独立，则x减y的方差为多少

Question

如题所述

Answer 1

根据方差的定义：
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)
当乘积：EXEY 为零时，
D(X-Y) = D(X) + D(Y)---------------------(2)
请再仔细推导一下！