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Correlation between XY and Y

  1. Nov 3, 2008 #1
    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....
     
  2. jcsd
  3. Nov 3, 2008 #2

    mathman

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    Gold Member

    Re: correlation

    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.
     
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