Consider an independent and identically distributed (iid) sample, X1,...., Xn, from a distribution with pdf (see attachment for equations). Use this information to answer the following questions:
a. Find the method of moments estimator of theta.
b. Find the maximum likelihood estimator of theta
c. Find the bias and mean squared error of the MLE.
d. Find the maximum likelihood estimator of the median of the distribution
e. Find a (possibly multidimensional) sufficient statistic for theta.
The solution illustrates the determination of method of moment estimator and maximum likelihood estimator for the parameter of distribution in step-by-step calculations. The properties of the estimator are also discussed thoroughly.