1. Consider the independent random variables X and Y defined below.
\begin{equation*}
F_X(x) = \begin{cases} 0, & x \le -2 \\ \frac{1}{2}(\frac{x}{2} + 1), & -2 \le x \le 2 \\ 1, & 2 \le x \end{cases}
\end{equation*}
,
\begin{equation*}
f_Y(y) = \begin{cases} \frac{1}{2}, & 1 \le y \le 3 \\ 0, & \text{otherwise} \end{cases}
\end{equation*}
a. Express and sketch the joint density function $f_{XY}(x, y)$.
