題組內容

2. (10%) Let $X_1, X_2, \ldots, X_n$ be a random sample from $U(0, \theta)$.

a. (5%) Find the shortest length \( 100(1 - \alpha)\% \) confidence interval for \( \theta \) in the class \( C(X) := \left[\frac{X_{(n)}}{\alpha}, \frac{X_{(n)}}{b}\right] \).