Mathematical statistics (Cramer-Rao, UMVUE)

Let X be one observation from a distribution with the probability density f(x|0) = 20 exp{-| |/0}. - 00 0 is unknown. Let +(0) = 1/(1 + 0) be the parameter function of interest. (a) Find the Cramer-Rao lower bound for an unbiased estimator of T(0). (b) Show that exp{-(X]} is the uniformly minimum variance unbiased estimator of T(0). (c) Find the variance of the estimator in (b). Does this variance attain the bound in (a)