Question: (20 points). Let ,.., X, be a random sample from the distribution of a random variable X with pdf: n f(x)= 2x (0.0)(x), 0>0.

(20 points). Let ,.., X, be a random sample from the distribution

(20 points). Let ,.., X, be a random sample from the distribution of a random variable X with pdf: n f(x)= 2x (0.0)(x), 0>0. (a) Show that = X2 is an unbiased estimator of . (b) Find the Cramer-Rao lower bound for the variance of = x. (c) Find the Fisher efficient estimator of 0. (d) Find the uniformly minimum variance unbiased estimator (UMVUE) of 0.

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