Question 5 (8 points) Let X denote the number of white balls selected when $k$ balls
are chosen at random from an urn containing $n$ white and $m$ red balls
(a) (2 points) Compute $P\{X = i\}$.
(b) (6 points) Let, for $i = 1, 2, \dots, k$; $j = 1, 2, \dots, n$,
$X_i = \begin{cases} 1, & \text{if the } i\text{th ball selected is white} \\ 0 & \text{otherwise} \end{cases}$
$Y_j = \begin{cases} 1, & \text{if white ball } j \text{ is selected} \\ 0 & \text{otherwise} \end{cases}$
Compute $E[X]$ in two ways by expressing $X$ first as a function of the $X_i$s and then
of the $Y_j$s.
