5. Let $X_{i}, \ldots, X_{n} \sim$ Uniform $(0, \theta $, where $\theta>0$ is an unknown parameter. Let $\hat{\theta}_{1}=2 X_{1}$ be an estimator for $\theta$. (a) (3 points) Find the MSE of $\hat{\theta}_{1}$. Moreover, is $\hat{\theta}_{1}$ unbiased or not? (b) (2 points) Use the Rao-Blackwell theorem to find a better estimator for $\theta$. What do we mean by "better" here? (c) (3 points) Is the estimator in (b) a UMVUE estimator? SP.DL.1731