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

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  • Schlemm, Eckhard

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.

Suggested Citation

  • Schlemm, Eckhard, 2013. "On the expected number of successes in a sequence of nested Bernoulli trials," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1619-1623.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:7:p:1619-1623
    DOI: 10.1016/j.spl.2013.03.018
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