IJPAM: Volume 88, No. 3 (2013)
A NEGATIVE BINOMIAL STOPPING TIME
Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101, USA
Abstract. A random walk moves upward or downward one unit at a time with probabilities and , respectively. We derive the averages of the maximum height and the minimum height attained before downward movements occur, and show the relationship between these average extrema and the average final height. We derive the limits of these average extrema as increases to , and derive the condition on that makes the average extrema symmetric about the initial height of .
Received: June 28, 2013
AMS Subject Classification: 60G50
Key Words and Phrases: simple random walk, average maximum height, negative binomial random variable, reflection principle
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DOI: 10.12732/ijpam.v88i3.7 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395