Suppose X1,X2,...,Xn is a random sample from a binomial distribution. Recall X is the number of successes in m independent trials with probability of success at each trial is θ. We know that E[X] = mθ and V ar(X) = mθ(1 −θ). (a) Find the method of moment estimator for θ. (b) Is the estimator in (a) unbiased? (c) Is the estimator in (a) consistent? (d) Show that the estimator in (a) is also the maximum likelihood estimator.

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