Let $X$ and $Y$ be two independent random variables. If $X$ and $Y$ are both standard normal, then what is the distribution of the random variable $$\frac{1}{2}(X^2+Y^2)$$
Is it right that the answer to this question is $$\frac{1}{2}(X^2+Y^2) \texttt{ ~ } EXP(1)$$? But how? Thank you very much, any help will be much appreciated.