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2. (a) Explain what is meant by a minimum variance unbiased estimator (MVUE). (b) Let X = (Xi, X2.... Xa) be a random sample from the distribution with probability density function: f(x;0) = 81 for OSIS 0 otherwise where 9 > 0 is an unknown parameter. i. You are given that 0 = X(m) = max(X1, X2. . ... X,) is the maximum likelihood estimator of 0. Determine the bis of this estimator of 9. ii. Derive an unbiased estimator of & by transforming X(); denoting this estimator 0. Show that O is an unbiased estimator of 0 and derive its variance. ifi. Is the estimator & you obtained in part ii, a consistent estimator of 0? Justify your