On the Count Probability of Many Correlated Symmetric Events

We consider \(N\) events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number of events that occur. If the probability of a single event...

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Bibliographic Details
Published in:arXiv.org 2019-10
Main Author: Kürsten, Rüdiger
Format: Article
Language:English
Subjects:
Characteristic functions
Exchanging
Probability distribution
Probability distribution functions
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Summary:We consider \(N\) events that are defined on a common probability space. Those events shell have a common probability function that is symmetric with respect to interchanging the events. We ask for the probability distribution of the number of events that occur. If the probability of a single event is proportional to \(1/N\) the resulting count probability is Poisson distributed in the limit of \(N\rightarrow \infty\) for independent events. In this paper we calculate the characteristic function of the limiting count probability distribution for events that are correlated up to an arbitrary but finite order.
ISSN:2331-8422