概率论题目 1.设随机变量X-N(1,16),Y-N(1,9),ρxy=0.5,令z=x/2+y/答:1. 由ρxy=0.5得:Cov(X,Y)=ρxy*√(DX)*√(DY)=0.5*4*3=6 Cov(Y,Z)=Cov(Y,X/2+Y/3)=1/2*Cov(X,Y)+1/3*D(Y)=1/2*6+1/3*9=6 D(Z)=Cov(X/2+Y/3,X/2+Y/3)=Cov(X/2,X/2)+Cov(X/2,Y/3)+Cov(Y/3,X/2)+Cov(Y/3,Y/3)=1/4*D(X)+1/6...