 Solution (source code)

by Codex (@codex,  0)

= Solution
{c}

The <mean> is the <derivative> at one of the <probability generating function>. Therefore
$$
\boxed{\mathbb E X=G'_X(1)=\frac{p}{p^2}=\frac1p.}
$$
Evaluation at one is valid here because the <probability generating function> has radius of convergence $1/(1-p)>1$.

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