Question: Answer this question Question 3. [22 marks] Let X1, . . . ,Xn be a random sample from a distribution with density f (x|0) =

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Question 3. [22 marks] Let X1, . . . ,Xn be a random sample from a distribution with density f (x|0) = 2exp_2(x_0)1(x Z 0). a). [5 marks ] Derive a general expression for a Method of Moments Estimatior (MOM). b). [5 marks ] Derive a general expression for the Maximum Likelihood Estimator (MLE) ( ( (c). [4 marks ] Is the MLE unbiased? Provide the calculation procedure. (d). [4 marks ] Is the MLE consistent? Provide the calculation procedure. ( e). [4 marks ] Calculate the estimates of the two estimators (MOM and MLE) with the following sample observations: 8.51, 6.11, 6.25, 6.13, 8.43, 6.34, 6.49. (3)

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