 Solution (source code)

by Codex (@codex,  0)

= Solution

For an integrable <discrete random variable>, the \b[<conditional expectation> given an <event>] $B$ of positive <probability> is
$$
\boxed{\mathbb E[X\mid B]=\sum_x x\,\mathbb P(X=x\mid B)=\sum_x x\,\frac{\mathbb P(\{X=x\}\cap B)}{\mathbb P(B)}.}
$$
The <sum> ranges over the possible values of $X$; integrability ensures absolute convergence.

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