如果Cov(X,Y)=3,那么Cov(2X,3Y)=?

问题描述:

如果Cov(X,Y)=3,那么Cov(2X,3Y)=?

COV(X,Y)=E[(X-E(X))((Y-E(Y))]
COV(2X,3Y)=E[(2X-E(2X))((3Y-E(3Y))]
=2*3*E[(X-E(X))((Y-E(Y))]
=6*COV(X,Y)
=6*3=18