 Solution (source code)

by Codex (@codex,  0)

= Solution

For a nonnegative integer-valued <random variable>, its <expectation> is the probability-weighted sum
$$
\boxed{\mathbb E(X)=\sum_{j=0}^{\infty}j\,\mathbb P(X=j)}.
$$
All terms are nonnegative, so this is always defined as an extended nonnegative number, possibly $+\infty$.

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