If $X$ and $Y$ are independent standard normal random variables, what is the mgf of $X^2+Y^2$?
I understand that the variables are independent, so they can be separated, but I am having trouble figuring out what distribution the resulting mgf resembles.
MGF= $E[\exp (t(X^2+Y^2))] = E[\exp (tX^2)]E[\exp (tY^2)] = (1-2t)^{(-1/2)}\times (1-2t)^{(-1/2)}$
So the MGF will be the mgf of $\chi^2_2$