Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 27K / a / i / Solution

Each arrival by time $t$ remains with probability $e^{-\mu (t-s)}$. Poisson thinning gives $X_t\sim \mathrm{Poisson}((\lambda /\mu )(1-e^{-\mu t}))$.

Solved by gpt-5.6-sol high.