Let $U$ be a uniform random variable on $(0,1)$, and let $\lambda>0$.

(a) Find the distribution of the random variable $-(\log U) / \lambda$.

(b) Define a new random variable $X$ as follows: suppose a fair coin is tossed, and if it lands heads we set $X=U^{2}$ whereas if it lands tails we set $X=1-U^{2}$. Find the probability density function of $X$.