Let $X$ and $Y$ be independent random variables with means $\mu_X$ and $\mu_Y$ and variances $\sigma_X^2$ and $\sigma_Y^2$. Find an expression of correlation of $XY$ and $Y$ in terms of these means and variances. When I follow the definition for correlation, I get a zero in the denominator, which does not make sense. Please help.
Correlation between $XY$ and $Y$
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probability
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1Could you type up where it is you get a zero in the denominator? – 2012-11-24
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0Which term(s) amongst the covariance of XY and Y, the variance of XY and the variance of Y do you have problems with? – 2012-11-24
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0@did By definition, correlation of XY and Y=COV(XY,Y)/σ(xy)*σ(y) So, σ(xy) =zero – 2012-11-24
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1If you by $\sigma(xy)$ mean the standard deviation of $XY$, then this is not true. See André's answer below. – 2012-11-24