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Let X and Y be two independent standard normal random variables. (a) Find the moment generating function of $X^2$. (b) Find the moment generating function of $XY$ . (c) Prove or disprove that $X^2$ and $XY$ have the same distribution.

Kinda confused as to how to do this. For a and b do you just calculate $E[e^{t(x^2)}]$ and $E[e^{t(xy)}]$? Or is there some other way of doing it. Also have no idea how to prove or disprove c.

Taha Akbari
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  • See http://math.stackexchange.com/questions/289347/finding-the-moment-generating-function-for-a-random-variable-x2 and http://math.stackexchange.com/questions/71516/moment-generating-function-of-the-chi-square-distribution – Behrouz Maleki Aug 10 '16 at 16:19

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