Let \(X_1\), \(X_2\), …, \(X_n\) be iid from some member of this parametric family:
\[ f(x\,|\,\theta) = \frac{1}{2\theta}\exp\left(-\frac{|x|}{\theta}\right), \quad -\infty<x<\infty. \]
- What is the maximum likelihood estimator of \(\theta>0\)?
- What is the sampling distribution of the estimator?
- What is the MSE of the estimator?
- Based on the MSE, what are the statistical properties of this estimator?