(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let X1 and X2 be independent random variables with nonzero variances. Find the correlation coefficient of Y = X1X2 and X1 in terms of the means and variances of X1 and X2.

2. Relevant equations

The answer is given as: [ m_{2}s_{1}] / [ sqrt( s_{1}^{2}s_{2}^{2}+ m_{1}^{2}s_{2}^{2}+ m_{2}^{2}s_{1}^2 )]

where m = mew

s = standard deviation

3. The attempt at a solution

E(Y) = E(X_{1}X_{2}) = E(X_{1})E(X_{2}) = m_{1}m_{2}

Var(Y) = E(X_{1}^{2}X_{2}^{2}) - m_{1}^{2}m_{2}^{2}

Cov(Y, X_{1}) = E(X_{1}^{2})E(X_{2}^{2}) - m_{1}^{2}m_{2}

which doesn't get me in the right direction to the answer...any helpful hints?

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# Homework Help: How to find correlation coefficient between two variables?

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