I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)E(XY)E(Y)
=E(XY^2)E(X)E(Y)^2.
If X and Y are independent, does it follow that X and Y^2 are independent. If this is the case, then covariance is zero > correlation is zero. If this isnt the case I'm really not sure how to proceed. Any help is appreciated....
