Consider these data:

\[ X_1,\,X_2,\,...,\,X_n\overset{\text{iid}}{\sim}\text{GF}(k,\,\theta). \]

So again, we are recycling the distribution family from Problem 13 above. Throughout, just treat \(k>0\) as fixed and known.

1. What is the maximum likelihood estimator of \(\theta\in\mathbb{R}\)?
2. What is the sampling distribution of the estimator?
3. What is the MSE of the estimator?
4. Based on the MSE, what are the statistical properties of this estimator?