Q4. (12 marks) Let $Y_1, Y_2, ..., Y_n$ be a random sample from the uniform distribution on the interval $(0, \theta)$, $0 < \theta$.
(1) Find the unbiased estimator of $\theta$ which is a function of the first order statistic $Y_{(1)}$.
(2) Calculate the variance of the estimator derived in (1).