I do my homework but I understand how to find the probability of this exercise, Could somebody give an idea or detail me.
The problem, let $X$ denote the number of white balls selected when $k$ balls are chosen at random from an urn containing $n$ white and $m$ black balls.
Let, for $i = 1, 2, \ldots, k; j = 1, 2, \ldots , n,$
$X_i=1$ if the $i^{th}$ ball selected is white, $0$ otherwise.
and $Y_i=1$ if the $j^{th}$ white ball is selected, $0$ otherwise.
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.
Then, we have to find first $E[X]=E[X_1]+E[X_2]+\cdots+E[X_k]$
and $E[X]=E[Y_1]+E[Y_2]+\cdots+E[Y_n]$.
That my question, how we find each $E[X_i]$ and $E[X_j]$?