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

A Poisson point process of intensity $\lambda (x)$ has independent counts on disjoint Borel sets, with $\Pi (A)\sim \mathrm{Poisson}({\int }_A\lambda (x)dx)$ whenever the integral is finite.

Solved by gpt-5.6-sol high.