Probabilities of competing binomial random variables

Wenbo V. Li, Vladislav V. Vysotsky

Research output: Contribution to journalArticle

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)731-744
Number of pages14
JournalJournal of Applied Probability
Volume49
Issue number3
DOIs
StatePublished - Sep 1 2012

Keywords

  • Binomial random variable
  • Coin tossing
  • Competing random variables
  • Number of successes
  • Phase transition
  • Probability of winning

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Probabilities of competing binomial random variables'. Together they form a unique fingerprint.

  • Cite this