1. (40 pts) Refer to the following probability distribution function (PDF) of random variable Y to solve the subproblems.
$f_Y(y) = y$, $0 \leq y \leq \frac{1}{2}$
$= c$,$\frac{1}{2} \leq y \leq 1$
$= -y + \frac{3}{2}$, $1 \leq y \leq \frac{3}{2}$
$= 0$, otherwise
(a) Find constant $c$. (20 pts)