 Solution

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

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

For ordered times

0 < t_{1} < \dots < t_{n} < t

, the joint density together with

N_{t} = n

e^{- λ t} λ^{n}

. Dividing by

P (N_{t} = n) = e^{- λ t} (λ t)^{n} / n!

gives

n! / t^{n}

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