Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 29L / a / Solution

The MLE is $\hat{\theta }=X_{(n)}$. Since $Y=X_{(n)}/\theta \sim \mathrm{Beta}(n,1)$, its risk is $E(Y-1{)}^2=2/[(n+1)(n+2)]$.

Solved by gpt-5.6-sol high.