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The first repetition of a pattern in a symmetric Bernoulli sequence

Published online by Cambridge University Press:  14 July 2016

Ehud D. Karnin
Ehud D. Karnin*
Affiliation:
Stanford University
*
∗ Postal address: Information Systems Laboratory, Department of Electrical Engineering, Stanford University, Stanford, CA 94305, U.S.A.
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Abstract

In a symmetric sequence of Bernoulli trials we define each successive l outcomes as a pattern, and look at the first time that any pattern repeats. Asymptotic expressions, as l →∞, of the distribution and the expectation of this waiting time are derived.

Keywords

REPEATED PATTERNSBIRTHDAY PROBLEM
Type
Short Communications
Information
Journal of Applied Probability , Volume 20 , Issue 2 , June 1983 , pp. 413 - 418
Copyright
Copyright © Applied Probability Trust 1983 

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Footnotes

This work was supported by the Joint Services Electronics Program under contract no. DAAG29-81-0057 and by the National Science Foundation under contract no. ECS79–16161.

References

[1] Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. 1, 3rd edn. Wiley, New York.Google Scholar
[2] Hellman, M. E. (1982) On DES based synchronous encryption. Computer Mag. Submitted.Google Scholar
[3] National Bureau Of Standards (1980) DES modes of operation. FIPS PUB 81, 2 December 1980.Google Scholar
[4] Sevastyanov, B. A. (1972) Poisson limit law for a scheme of sums of dependent random variables. Theory Prob. Appl. 17, 695–699.Google Scholar
[5] Zubkov, A. M. and Mikhailov, V. G. (1974) Limit distribution of random variables associated with long duplications in a sequence of independent trials. Theory Prob. Appl. 19, 172–179.Google Scholar