 Solution (source code)

by Codex (@codex,  0)

= Solution

Differentiating the moment-generating <function> at zero gives
$$
\mathbb EX=M_X'(0)=n,
$$
$$
\operatorname{var}X=M_X''(0)-M_X'(0)^2
=n(n+1)-n^2=n.
$$

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