 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ib/paper-2/6h/a/solution

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

The likelihood is

θ e^{- θX}

. Multiplication by the prior gives a density proportional to

θ^{m} e^{- (λ + X) θ}

, so

θ ∣ X \sim Γ (m + 1, λ + X)

in shape-rate parametrisation.

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