Statement of a problem № m41162


Consider an infinite sequence of Bernoulli trials for which the parameter p is unknown (0 < p < 1), and suppose that sampling is continued until exactly k successes have been obtained, where k is a fixed integer (k ≥ 2). Let N denote the total number of trials that are needed to obtain the k successes. Show that the estimator (k − 1)/(N − 1) is an unbiased estimator of p.

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