Communications in Information and Systems

Volume 16 (2016)

Number 1

A note on the number of long runs

Pages: 59 – 81

DOI: http://dx.doi.org/10.4310/CIS.2016.v16.n1.a3

Authors

S. Nguyen (Department of Mathematics and Statistics, Texas Tech University, Lubbock, Tx., U.S.A.)

X. Wang (Department of Mathematics and Statistics, Texas Tech University, Lubbock, Tx., U.S.A.)

C. Martin (Department of Mathematics and Statistics, Texas Tech University, Lubbock, Tx., U.S.A.)

Abstract

In this paper we present a simple derivation of the probability of attaining a run of $r$ heads when tossing a coin $n$ times. We use this result to establish other properties of coin tossing. Using the same techniques we find the probability of runs of either heads or tails. We give a complete analysis of both recurrences. In addition we construct the generating functions for the recurrences.

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