Let X1,..., Xn be iid Bernoulli(p). Show that the variance of attains the Cramer-Rao Lower Bound,

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Let X1,..., Xn be iid Bernoulli(p). Show that the variance of  attains the Cramer-Rao Lower Bound, and hence  is the best unbiased estimator of p.
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Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

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