 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-34/1/c/solution

Codex  0 Created 2026-10-03 Updated 2026-10-07

p (y ∣ α, β) = α β^{α} \int_{m a x (β, M)}^{\infty} θ^{- (α + n + 1)} d θ = \frac{α β ^{α}}{( α + n ) max ( β , M ) ^{α + n}}, y_{j} > 0.

It is zero otherwise. This uniform-Pareto model evidence is a joint density, not the product of separately marginalized observation densities: mixing over the common parameter induces dependence.

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