I have a question regarding covariance.
If we have two independent variables $X$ and $Y$, then is the $Cov(X^n, Y^m) = 0$ with arbitrary values of $n$ and $m$?
I know that $Cov(X^n,Y^m) = E(X^nY^m) - E(X^n)E(Y^m)$ but I can't derive $E(X^nY^m)$.
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Are you talking about raising variables (X & Y) to powers (n & m)? – gung - Reinstate Monica Mar 19 '15 at 02:57
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@gung I'm almost certain that's the intent. – Glen_b Mar 19 '15 at 05:29
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This result follows immediately upon applying http://stats.stackexchange.com/questions/94872/functions-of-independent-random-variables to conclude $X^n$ and $Y^m$ are independent, whence their covariance must be zero. – whuber Mar 19 '15 at 14:27