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Extensions of the Hájek–Rényi inequality to moments of higher order

Published online by Cambridge University Press:  24 October 2008

J. E. A. Dunnage
J. E. A. Dunnage
Affiliation:
Chelsea College of Science and Technology, London SW3 6LX
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Extract

1. Introduction. Bernoulli trials. Consider a sequence of Bernoulli trials. Let p, assumed to satisfy 0<p < 1, be the probability of success at any given trial and let q = 1–p. If Nn is the number of successes in the first n trials, it is well known that Nn/n→p almost surely as n→∞ so that for every ∈> 0,

as n→∞, and it is clearly of great interest to know quantitatively how this probability depends upon n and ∈.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 72 , Issue 1 , July 1972 , pp. 67 - 75
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

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