Solution
= Solution
Independence gives
$$
M_S(t)=\prod_{j=1}^nM_{X_j}(t)
=\left[\exp(e^t-1)\right]^n
=\exp\{n(e^t-1)\}.
$$
This is the moment generating <function> of a <Poisson distribution> with mean $n$. Hence
$$
\boxed{S\sim\operatorname{Poisson}(n)}.
$$