= Solution
The <acceptance mass for an unnormalized rejection envelope> follows by integrating the proposal-specific acceptance <probability>:
$$
\boxed{p_{\rm acc}=\mathbb E_g\!\left[\frac{f(Y)}{Mg(Y)}\right]
=\frac CM.}
$$
The inequality $f\leq Mg$ also gives $C\leq M$, so this is a valid <probability>. It is the same at every <independent> trial.
If $J_i$ indicates acceptance of the $i$th proposal, then $J_1,\ldots,J_n$ are <independent> <Bernoulli distribution> variables with parameter $C/M$. Hence the accepted count $K=\sum_iJ_i$ satisfies
$$
K\sim\operatorname{Bin}\!\left(n,\frac CM\right),
\qquad
\boxed{\mathbb EK=\frac{nC}{M}=\frac nM\int_{\mathbb R}f(y)\,dy.}
$$
Its <variance> is $np_{\rm acc}(1-p_{\rm acc})$. Conditional on any acceptance pattern, the accepted values have <independent> target <probability density function> $h$; mixing over patterns retains this product law conditional on their count.
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