Question
3. Let Y1,..., Yn denote a random sample of discrete random variables from the following probability mass function P(Y = -1) = 0 P(Y
3. Let Y1,..., Yn denote a random sample of discrete random variables from the following probability mass function P(Y = -1) = 0 P(Y = k) = (1-0)20k for k = 0, 1, 2, .. for the unknown parameter 0 < 0 < 1. (a) Find the method of moment estimator MME of 0. Is this estimator unbiased? (b) Find the maximum likelihood estimator MLE of 0. Is this estimator unbiased? (c) Find the Fisher information number. What is the smallest possible variance that could be achieved by an unbiased estimator of 0 in this case?
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