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On a general probability theorem and its applications in the theory of the stochastic processes

Published online by Cambridge University Press:  24 October 2008

Lajos Takács  and
W. L. Smith
Lajos Takács
Affiliation:
Research Institute for Mathematics, Hungarian Academy of Sciences, Budapest, Hungary
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Extract

Let us consider an experiment, the possible outcomes of which are random events. Let A1, A2, …, An be some of these outcomes. Define the random variable ηn as the number of the events occurring simultaneously among the A1, A2, …, An in an experiment. Denote by Pk = (ηn = k) (k = 0,1, 2, …, n), the distribution of the random variable ηn and by , the binomial moments of ηn. Here is the symbol of the probability and & that of the expectation.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 219 - 224
Copyright
Copyright © Cambridge Philosophical Society 1958

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