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On Two Problems Involving Partial Sums

Published online by Cambridge University Press:  27 July 2009

Mar Brown
Mar Brown
Affiliation:
Department of MathematicsMThe City College, The City University of New York New York, New York 10031
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Abstract

Two problems are considered: (1) The expected waiting time for the partial sums of i.i.d. positive integer-valued random variables to be a multiple of k for the first time. For aperiodic distributions this expected value is shown to equal k. The periodic case is considered, as well as the waiting time for the partial sums to equal r modulo k. (2) For two independent sequences of partial sums of positive i.i.d. random variables, the expected value of the smallest common partial sum is derived. If both distributions are aperiodic, this expected value is the product of the two means. The periodic case is considered, as well as the case of more than two sequences.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 3 , Issue 4 , October 1989 , pp. 511 - 516
Copyright
Copyright © Cambridge University Press 1989

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References

Feller, W. (1968). An introduction to probability theory and its applications, Vol. I, 3rd edition. New York: John Wiley.Google Scholar
Ross, S.M. (1983). Stochastic processes. New York: John Wiley.Google Scholar