 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ii/paper-2/29j/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

The Kolmogorov-Smirnov theorem states that, for continuous

F

n sup_{x} ∣ F_{n} (x) - F (x) ∣ d sup_{0 \leq t \leq 1} ∣ B (t) ∣,

where

B

is a Brownian bridge; the finite-sample law is also independent of continuous

F

H_{0} : F = F_{0}

, compute

D_{n} = sup_{x} ∣ F_{n} (x) - F_{0} (x) ∣

and reject when

n D_{n}

exceeds the appropriate null quantile.

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