Question

随机变量X~N(0,1),B(10,0.5),且X与Y不相关,则 E(X-Y)=?D(X-Y)=?

Answer 1

E(X-Y)=EX-EY=0-10=-10

D(X-Y)=D(X)+D(Y)-2Cov(X,Y)

因为X与Y不相关,所以Cov(X,Y)=0

所以D(X-Y)=D(X)+D(Y)=1+0.5^2=1.25