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One of two independent Bernoulli processes (arms) with unknown expectations and is selected and observed at each of n stages. The selection problem is sequential in that the process which is selected at a particular stage is a function of the results of previous selections as well as of prior information about and. The variables and are assumed to be independent under the (prior) probability distribution. The objective is to maximize the expected number of successes from the n selections. Sufficient conditions for the optimality of selecting one or the other of the arms are given and illustrated for example distributions. The stay-on-a-winner rule is proved.
Donald A. Berry (Thu,) studied this question.