On fair coin-tossing games

Robert Chen, Alan Zame

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Let Ω be a finite set with k elements and for each integer n ≧ 1 let Ωn = Ω × Ω × ... × Ω (n-tuple) and Ωn = {(a1, a2,..., an) | (a1, a2,..., an) ∈ Ωn and aj ≠ aj+1 for some 1 ≦ j ≦ n - 1}. Let {Ym} be a sequence of independent and identically distributed random variables such that P(Y1 = a) = k-1 for all a in Ω. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in Ωn and in Ω̄n with respect to the stochastic process {Ym}. The results here provide us with a better and deeper understanding of the fair coin-tossing (k-sided) process.

Original languageEnglish (US)
Pages (from-to)150-156
Number of pages7
JournalJournal of Multivariate Analysis
Volume9
Issue number1
DOIs
StatePublished - Mar 1979

Keywords

  • fair coin-tossing game
  • fair coin-tossing process
  • stopping time
  • the Conway Algorithm
  • the renewal theorem
  • the taboo first passage probability

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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