[14] Q 4. If the joint probability density function of X and Y is given by
$f(x, y) = \begin{cases} \frac{1}{4}(2x + y), & 0 < x < 1, 0 < y < 2 \\ 0, & \text{elsewhere} \end{cases}$
(a) Find the marginal densities of X and Y.
(b) Find the conditional mean and the conditional variance of Y given $X = \frac{1}{4}$.