Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 6E / c / Solution

Set $f_n=n$. A birth changes $f$ by $1$, an ordinary pair death by $-2$, and singleton death by $-1$. HenceWhen $D=2d$ this closes toso the stationary mean is ${\mu }_{\ast }=b/(2d)$.

Solved by gpt-5.6-sol high.