Let $S = \sum_{i=1}^{N} X_i.$
$\mathbb EX = 1, \mathbb DX = 2.$
$N$ has a negative binomial distribution with parameters $k=80$ and $p=0.4.$
$$\mathbb P(N=l)=\begin{pmatrix} k+l-1 \\ l \\ \end{pmatrix} p^kq^l, l=0,1,2,.. .$$ Find $\mathbb ES = (\mathbb EN)( \mathbb EX).$
(The answer is 120.)
How to find $(\mathbb EN)$?