 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2013/iii/paper-34/2/d/solution

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

For

τ = c σ

with

c > 0

p_{τ} (τ) \propto p_{σ} (τ / c) / c = (τ / c)^{- 1} / c = τ^{- 1} .

Equivalently,

\frac{d ( c σ )}{c σ} = \frac{d σ}{σ} .

(0, \infty)

diverges, it is an improper prior, not a normalized probability distribution on that range.

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