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On the number of uniform random variables which must be added to exceed a given level

Published online by Cambridge University Press:  14 July 2016

K. G. Russell
K. G. Russell*
Affiliation:
Victoria University of Wellington
*
∗ Postal address: Department of Mathematics, Victoria University of Wellington, Private Bag, Wellington, New Zealand.
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Abstract

This note obtains the distribution of N(a), the number of independent random variables each distributed uniformly on (0, 1) which must be added for the sum first to exceed some positive constant a.

Keywords

SUMEXCEEDANCEAPPLICATIONS
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 1 , March 1983 , pp. 172 - 177
Copyright
Copyright © Applied Probability Trust 1983 

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References

Feller, W. (1971) An Introduction to Probability Theory and its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Gnedenko, B. V. (1976) The Theory of Probability, 3rd edn. MIR Publishers, Moscow.Google Scholar
Hansen, E. R. (1975) A Table of Series and Products. Prentice-Hall, Englewood Cliffs, N.J. Google Scholar