General Linear Hypotheses

Let \(X_1,\ldots ,X_n\) be a random sample from \(\operatorname {Uniform}[0,\theta ]\). Find the UMP test of size \(\alpha \) of \(H_0:\theta \geq \theta _0\) vs. \(H_a:\theta <\theta _0\) by first deriving a most powerful test of simple hypotheses and then extending it to composite hypotheses.