Question (Sufficient statistic \( \left[5\right. \) marks ]). Assume \( X_{1}, \cdots, X_{n} \) is a random sample from a uniform distribution on the interval \( [0, \theta] \), where \( \theta \) is the unknown parameter. Show that \( \max \left(X_{1}, \cdots, X_{n}\right) \) is a sufficient statistic for \( \theta \).