Let $X_1, \dots, X_n$ be a sample from a distribution with probability density
$\rho_\theta(x) = \theta x^{-2}$ for $x \ge \theta$
and 0 for $x < \theta$, with $\theta > 0$ unknown.
(i) Determine the maximum likelihood estimator for $\theta$.
(ii) Is this estimator unbiased?
(iii) Determine the mean square error of this estimator.
