题目
Given that x and y are random variables, and a, b, c and d are constant, which one of the following definitions is wrong?
选项
A.E(ax+by +c) = aE(x) + bE(y) + c, if x and y are correlated.
B.Var(ax+by +c) = Var(ax+by) + c, if x and y are correlated.
C.Cov(ax+by,cx+dy) = acVar(x) + bdVar(y) + (ad+bc)Cov(x,y), if x and y are correlated.
D.Var(x-y) = Var(x+y) = Var(x) + Var(y), if x and y are uncorrelated.
答案
B
解析
VaR(ax+by+c)=VaR(ax+by)=a2 VaR(x)+b2 VaR(y)+2abCov(x,y) 本题解析如下： VaR(ax by c)=VaR(ax by)=a2 VaR(x) b2 VaR(y) 2abCov(x,y)