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#1

Let X be a single observation from N(0, 0). (0 =02.) (a) Is X a sufficient statistic? (b) Is | X) a sufficient statistic ? (c) Is X2 an unbiased estimator of 0? (d) What is a maximum-likelihood estimator of V 0? (e) What is a method-of-moments estimator of v 0?Let X1, X2, ...; Xn be a random sample from the density f(x; 0) =0x-2 I(6, w)(x) where 0 > 0. (a) Find a maximum-likelihood estimator of 0. (b) Is Y, = min [X1, ..., X,] a sufficient statistic