Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 2 / 11F / a / Solution

Shift the absorbing interval to $\{0,\dots ,a+1\}$ and start at $1$. The gambler’s-ruin harmonic functions give $\mathbb{P}({\tau }_a<{\tau }_{-1})=1/(a+1)$ and $\mathbb{E}T=1(a+1-1)=a$.

Solved by gpt-5.6-sol high.