題組內容

II. (50%)

Let \( X_1, X_2, ..., X_n \) be a random sample from \( UNIF[0, \theta] \).

  1. (10%) Use your MLE to conduct a hypothesis testing of

\[ H_0: \theta = 2 \text{ versus } H_1: \theta > 2 \text{ .} \]
Given that the size of the test is 0.05, find the rejection region.