Is the Correlation between XY and Y Zero if X and Y are Independent?

[rhuelu]

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 isn't the case I'm really not sure how to proceed. Any help is appreciated...

 

[mathman]

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 isn't the case I'm really not sure how to proceed. Any help is appreciated...

X and Y^2 are independent. However your formula has cov(XY,Y)=E(X)[E(Y^2)-E(Y)^2] which is not 0, unless E(X)=0.