Probabilities of Competing Binomial Random Variables
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Published:2012-09
Issue:3
Volume:49
Page:731-744
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ISSN:0021-9002
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Container-title:Journal of Applied Probability
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language:en
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Short-container-title:Journal of Applied Probability
Author:
Li Wenbo V.,Vysotsky Vladislav V.
Abstract
Suppose that both you and your friend toss an unfair coin n times, for which the probability of heads is equal to α. What is the probability that you obtain at least d more heads than your friend if you make r additional tosses? We obtain asymptotic and monotonicity/convexity properties for this competing probability as a function of n, and demonstrate surprising phase transition phenomenon as the parameters d, r, and α vary. Our main tools are integral representations based on Fourier analysis.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Reference8 articles.
1. [2] Dong Z. , Li W. V. and Song C. (2011). Integral representations for binomial sums of chances of winning. In preparation.
2. CRC Standard Mathematical Tables and Formulae
3. How to lose as little as possible;Addona;Ars Math. Contemp.,2011