consider the

3. Consider a random sample of size n {X,..., X } from a random variable X having density f ( x; 0 ) = (In ) Ox! x = 0, 1, ..., 0>1. (a) Show that X belongs to the regular exponential class and hence find a complete sufficient statistic for 0. (4 marks) (b) Find the CRLB for the variances of unbiased estimators of 0. (5 marks) (c) Find the CRLB for the variances of unbiased estimators of (In 0)2. (3 marks) (d) Find the UMVUE of (In 0) . Note that your estimator should be based on all observations of the random sample. (8 mark)