Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 6H / a

A statistic $T(X)$ is sufficient for a parameter $\theta$ when the conditional distribution of the full sample $X$ given $T$ does not depend on $\theta$. For a dominated model, the Fisher-Neyman factorization theorem says this is equivalent to a factorizationwhere $h$ is independent of $\theta$.