1. Let $X_1, \dots, X_n$ be a random sample from a population with pdf
(a) Find $\hat{\theta}$, the MLE of $\theta$
$f(x|\theta) = \frac{1}{2\theta}, -\theta < x < \theta, \theta > 0$
(b) Let $Y = \hat{\theta}$, the MLE of $\theta$: Find the pdf of Y.
(c) Prove Y is a sufficient statistic for $\theta$.
(d) Find, if one exists, a UMVUE of $\theta$.