概率（正态分布）设二维随机变量(X,Y)服从二维正态,则随机变量a=X+Y与b=X-Y独立的充分必要条件为:DX=DY如何证明

X,Y are normal distributed,so that X+Y,X-Y are parewise independent iff cov(X+Y,X-Y)=0,namelycov(x,x)+cov(X,Y)-cov(X,Y)-cov(Y,Y)=0,and consequently D(X)=cov(X,X)=cov(Y,Y)=D(Y)