 Solution

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

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

p (θ ∣ y) \propto θ^{- (α + n) - 1} 1_{{θ > m}}, m = max (β, M) .

The integral of this kernel is

m^{- (α + n)} / (α + n)

, so the normalized posterior distribution is

p (θ ∣ y) = (α + n) m^{α + n} θ^{- (α + n) - 1} 1_{{θ > m}} .

Thus it is

Pareto (α + n, m)

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