Question: Let \({{X}_{1}},...,{{X}_{n}}\) be a random sample from Gamma(1, \(\lambda \) ) distribution. [The pdf function

for Gamma distribution can be found in Appendix I.]

(a) Find the Maximum Likelihood Estimator of (8 points)

(b) Is the MLE estimator unbiased? (4 points)

(c) Calculate the mean squared error of the MLE estimator (8 points)