为什么协方差cov(x,-y)= -cov(x,y)

问题描述:

为什么协方差cov(x,-y)= -cov(x,y)

Cov(X,Y)=E(XY)-E(X)E(Y),
cov(x,-y)=E[X(-Y)]-E(X)E(-Y)=-E(XY)+E(X)E(Y)=-Cov(X,Y)