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On fair coin-tossing games

Author

Listed:
  • Chen, Robert
  • Zame, Alan

Abstract

Let [Omega] be a finite set with k elements and for each integer n [greater, double equals] 1 let [Omega]n = [Omega] - [Omega] - ... - [Omega] (n-tuple) and 11 and aj [not equal to] aj+1 for some 1 [less, double equals] j [less, double equals] 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 [Omega]. In this paper, we obtain some very surprising and interesting results about the first occurrence of elements in [Omega]n and in [Omega]n 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.

Suggested Citation

  • Chen, Robert & Zame, Alan, 1979. "On fair coin-tossing games," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 150-156, March.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:1:p:150-156
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    Cited by:

    1. Emilio De Santis & Fabio Spizzichino, 2016. "Some Sufficient Conditions for Stochastic Comparisons Between Hitting Times for Skip-free Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1021-1034, December.
    2. Emilio De Santis & Yaakov Malinovsky & Fabio Spizzichino, 2021. "Stochastic Precedence and Minima Among Dependent Variables," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 187-205, March.

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