 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2002/iii/paper-40/2/b/iii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

For

x \geq k

, the proposal CDF is

G (x) = 1 - k / x

V \sim U (0, 1)

gives

X = G^{- 1} (V) = \frac{k}{1 - V} .

Equivalently, put

U = 1 - V

, which is also uniform, and use $X = k / U$ . This equivalent parametrization matches the uniforms used in the final estimator.

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