Question

Question 3 15 marks] Let X1,..,X be independent identically distributed random variables with pdf common ) = { (#)%2-1/64 0 fx (a;e) 0 where 0 >0 is an unknown parameter X-1. Show that Y ~ T (}, ); (a) Let Y (b) Show that 1 T n =1 is an unbiased estimator of 0-1 ewhere / (0; X) is the log- likeliho od function; (c) Compute U - (d) What functions T (0) have unbiased estimators that attain the relevant Cramér-Rao lower bounds (CRLB)? (e) Derive the CRLB for the variance of unbiased estimators of T (0) = 0-1; (f) Find a complete and sufficient statistic for f. Show all reasoning; (g) Find the unique minimum variance unbiased estimator of 0-1,T, and compute its variance

Answer 1

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