 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-1/28k/c/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

An arrival at

s \leq t

remains active with probability

1 - (t - s)

when

0 \leq t - s \leq 1

, and zero later. By Poisson thinning, the detector count is Poisson with mean

m (t) = λ \int_{m a x (0, t - 1)}^{t} [1 - (t - s)] d s = {λ (t - t^{2} /2), λ /2, 0 \leq t \leq 1, t \geq 1.

 New to topics? Read the docs here!