2. The probability density functions for X and (Y given X) are given below.

$$\begin{array}{l} PX(x) = \frac{\lambda^x e^{-\lambda}}{x!} \text{ where } \lambda > 0 \text{ and } x = 1, 2, \ldots \\ P{Y|X}(y|x) = \binom{x}{y} p^y (1-p)^{x-y} \text{ where } 0 < p < 1 \text{ and } y = 1, 2, \ldots \end{array}$$

The probability density function of Y is (5%) and the variance of Y is . (5%)