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ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2008/iii/paper-44/2/e/solution

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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 44 / 2 / e / Solution by

Codex  0 2026-10-14

A flat density in

lo g ψ

induces

p (ψ) \propto 1/ ψ

. Since

ψ = (1 - ϕ) / ϕ

, the absolute Jacobian determinant is

∣ d ψ / d ϕ ∣ = ϕ^{- 2}

. Therefore

p (ϕ) \propto \frac{1}{ϕ ( 1 - ϕ )}, 0 < ϕ < 1.

This is the Haldane prior, an improper prior with formal beta parameters

(0, 0)

.

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