Let \(X_1\), \(X_2\), …, \(X_n\) be iid from some member of the parametric family that you met on Midterm 2:

\[ f(x\,|\,\theta)=\theta(x+1)^{-(\theta+1)},\quad x>0. \]

1. What is the maximum likelihood estimator of \(\theta>0\)?
2. What is the sampling distribution of the estimator? Problem 14 might be helpful here.
3. What is the MSE of the estimator?