Let $X_1, X_2, ..., X_n$ be an iid random sample of size $n$ from an Exponential($\theta$) distribution with probability density function
$f(x; \theta) = \frac{1}{\theta}e^{-x/\theta}, \quad x > 0, \quad \theta > 0.$
(a) Find the maximum likelihood estimator for $\theta, \hat{\theta}$. Then using that result, calculate the estimate when $x_1 = 14, x_2 = 25$, and $x_3 = 18$. (This will be a number.)
(b) The mean squared error (MSE) of an estimator $\hat{\theta}$ is defined as $MSE(\hat{\theta}) = [Bias(\hat{\theta})]^2 + Var(\hat{\theta})$.
Calculate the value of the bias of the maximum likelihood estimator for $\theta, \hat{\theta}$. (That will be a
