Find the Maximum Likelihood Estimator of B
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Find the Maximum Likelihood Estimator of B

Question 3:

Let X1, X2,..., Xn be iid observations from Gamma(1,B) distribution where a = 1.The pdf of X is given by


a) Find the Maximum Likelihood Estimator of B

b) Is the MLE estimator unbiased? (hint: you may use the sum of the gamma distribution is still gamma distribution.)

c) Calculate the mean squared error of the MLE estimator.


Hint
Most often, the maximum likelihood estimators are biased, therefore it is important to approximate the expected bias in order to lessen the mean square errors of the parameter estimates. Specified the data MLE for the parameter p is the value of p that make best use of the likelihood P...
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