I've been working on this problem all day but, honestly I don't know what else to try.
Let Z~N(0,1) and
find (Correlation coefficient
I think I need to find the the joint PDF of X and Y then calculate the Cov(XY), maybe this will let me cancel what's left of the denominator and obtain a number. I'm quite lost.
I should probably mentioned that i tried the linear properties of expectation and arrived to the conclucion that it was not correlated but i think my application is wrong.