For each of the following find the probability density function of Y. Do not forget the specify the
domain of Y!
(a) [2 points] Y = X$^2$ and $f_x(x) = 1$, $0 < x < 1$
(b) [2 points] Y = -log X and X has pdf
$f_x(x) = \frac{(n + m + 1)!}{n!m!}x^n(1 - x)^m$, $0 < x < 1$, $m$, $n$ postive integers
(c) [2 points] Y = $e^x$ and X has pdf
$f_x(x) = \frac{1}{\sigma^2}xe^{-(x/\sigma)^2/2}$, $0 < x < \infty$, $\sigma^2$ a postive constant
(d) [2 points] Y = $|X|^3$ and $f_x(x) = \frac{1}{2}e^{-|x|}$, $-\infty < x < \infty$.
