 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-4/27k/c/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

r \leq R

if its uniform radius exceeds

r

1 - r / R

. Marked Poisson thinning gives a Poisson count with mean

2 πλ \int_{0}^{R} r (1 - r / R) d r = λπ R^{2} /3.

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