1. Let X and Y be two jointly continuous random variables
with joint PDF
$\begin{equation*}
f_{XY}(x, y) = \begin{cases}
\frac{x^2}{4} + \frac{x^2}{4} + \frac{xy}{6} & 0 \le x \le 1, 0 \le y \le 2 \\
0 & \text{otherwise}
\end{cases}
\end{equation*}$For $0 \le y \le 2$, find
a. the conditional PDF of X given Y = y;
b. $P(X < \frac{1}{2} | Y = y)$.
