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.