Acceptance mass for an unnormalized rejection envelope ($p_{\mathrm{acc}}=C/M$)

If $f\ge 0$, $C=\int f\in (0,\infty )$ and $f(x)\le Mg(x)$ for a proposal probability density function $g$, accept a proposal $Y$ when an independent uniform distribution value is at most $f(Y)/(Mg(Y))$. Integrating the joint acceptance probability density function gives $p_{\mathrm{acc}}=C/M$ and conditional accepted probability density function $f/C$. For $n$ independent proposals the accepted count has binomial distribution with parameters $n,C/M$.