Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 6H / a / Solution

Factorisation of the likelihood $(1-\theta {)}^{-n}{1}_{\{\theta \le X_{(1)}\}}$ shows that $T=X_{(1)}$ is sufficient: conditional on it, the sample law is independent of $\theta$.

Solved by gpt-5.6-sol high.