On the expected number of successes in a sequence of nested Bernoulli trials

Eckhard Schlemm

Statistics & Probability Letters, 2013, vol. 83, issue 7, 1619-1623

Abstract: We analyse the asymptotic behaviour of the probability of observing the expected number of successes at each stage of a sequence of nested Bernoulli trials. Our motivation is the desire to give a genuinely frequentist interpretation for the notion of probability based on finite sample sizes. The main result is that the probabilities under consideration decay asymptotically as n−1/3, where n is the common length of the Bernoulli trials. The main ingredient in the proof is a new fixed-point theorem for non-contractive symmetric functions on the unit interval.

Keywords: Bernoulli trials; Expectation; Fixed-point theorem; Frequentism (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1016/j.spl.2013.03.018

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