Question: (b) Let {X1, X2, . .., Xa} be a random sample from the probability distribution with probability density function: f ( 2:0) (0 ' for

(b) Let {X1, X2, . .., Xa} be a random sample from the probability distribution with probability density function: f ( 2:0) (0 ' for - 20 0 is an unknown parameter i. Derive the method of moments estimator of 0. (4 marks) ii. Is the estimator of 0 derived in part i. biased or unbiased? Justify your answer. Hint: You may use the fact that E(X ) = E(X). (3 marks) iii. Given that the variance of the method of moments estimator of 0 in part i. is 0/(27n), check whether the estimator is a consistent estimator of 0

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