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arXiv · 1303.4979

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

Eckhard Schlemm
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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 attempt to give a genuinely frequentist interpretation to 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 of the unit interval.

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Eckhard Schlemm. 2013-03-20. On the expected number of successes in a sequence of nested Bernoulli trials. https://doi.org/10.1016/j.spl.2013.03.018

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