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A theorem on the cumulative product of independent random variables

Published online by Cambridge University Press:  24 October 2008

Harold Ruben
Harold Ruben
Affiliation:
Manchester UniversityEngland Columbia UniversityNew York
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Extract

1. Introductory discussion and summary. Consider a sequence {ui} of independent real or complex-valued random variables such that E(ui) = 1, and a sequence of mutually exclusive events S1, S2,…, such that Si depends only on u1, u2, …,ui, with ΣP(Sj) = 1. Define the random variable n = n(u1, u2,…) = m when Sm occurs. We shall obtain the necessary and sufficient conditions under which

referred to as the product theorem.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 4 , October 1959 , pp. 333 - 337
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

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