A <Poisson point process>[Poisson random measure] $N$ of intensity $\mu$ assigns to disjoint measurable sets independent random variables, and
$$
N(A)\sim\operatorname{Poisson}(\mu(A))
$$
whenever $\mu(A)<\infty$, with the usual countable-additivity requirement.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 201 / 6 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-201/6/a/solution