1. Let {X1, X2, ... , Xn} depict a set of sample random variables drawn from a N(θ , 1) population. Find a best unbiased estimator of θ 2. Does the variance of this estimator attain the Cramér-Rao lower bound?
2. Let X1, ... , Xn depict a random sample drawn from the probability density function f (x; θ) = θxθ -1,0 x 1, θ > 0. Find the minimum variance bound for an unbiased estimator of θ .