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Journal of Probability and Statistics
Volume 2010, Article ID 279154, 16 pages
Research Article

A Winner's Mean Earnings in Lottery and Inverse Moments of the Binomial Distribution

1UCD CASL, University College Dublin, Belfield, Dublin 4, Ireland
2School of Electronic, Electrical & Mechanical Engineering, University College Dublin, Dublin 4, Ireland

Received 5 November 2009; Revised 30 January 2010; Accepted 16 February 2010

Academic Editor: Daniel Zelterman

Copyright © 2010 Konstantinos Drakakis. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We study the mean earnings of a lottery winner as a function of the number 𝑛 of participants in the lottery and of the success probability 𝑝 . We show, in particular, that, for fixed 𝑝 , there exists an optimal value of 𝑛 where the mean earnings are maximized. We also establish a relation with the inverse moments of a binomial distribution and suggest new formulas (exact and approximate) for them.