 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/17h/a/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 4 / 17H / a / Solution by

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

A statistic is sufficient when the conditional law of the sample given it is parameter-free; it is minimal sufficient when it is a function of every sufficient statistic. The likelihood factors as

L = [π + (1 - π) e^{- λ}]^{n_{0}} (1 - π)^{n - n_{0}} e^{- λ (n - n_{0})} λ^{S} \prod_{i} \frac{1}{X _{i} !},

(1)

so the factorization theorem makes

(n_{0}, S)

sufficient. The likelihood-ratio criterion shows that the ratio for two samples is parameter-independent exactly when both

n_{0}

and

S

agree. Thus

(n_{0}, S) is minimal sufficient .

(2)

 Read the full article

 New to topics? Read the docs here!