Question: Question 2 Consider a random sample X1, X2, ..., Xn from a distribution with pdf given by 2x f (x) = Oxse 0, elsewhere Let

Question 2 Consider a random sample X1, X2, ..., Xn from a distribution with pdf given by 2x f (x) = Oxse 0, elsewhere Let 01 = = X and 02 = Yn be estimators of 0, where X is the sample mean and Y = max(X1, X2, ..., Xn). (a) Show that 0, is unbiased estimator for 0. (6 marks) (b) Show that 02 is a biased estimator of 0. (5 marks) Page 1 of 3 May - Aug. 2021 Final Examination AS106 Mathematical Statistics (c) Construct an estimator 03 based on Y, that is unbiased. (2 marks) (d) Between 0, and 03, which estimator is more efficient? (12 marks)

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