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