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Coin tossing, revisited

Published online by Cambridge University Press:  14 July 2016

O. E. Percus  and
J. K. Percus
O. E. Percus*
Affiliation:
New York University
J. K. Percus*
Affiliation:
New York University
*
∗ Postal address: Courant Institute of Mathematical Sciences
∗ Postal address: Courant Institute of Mathematical Sciences
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Abstract

An iterated sequence of Bernoulli trials is carried out and the success probability estimated at each point on the sequence by the current success ratio. We find the probability P1 that this estimate always lies above some pre-selected rational fraction p′, and its complement P2, the probability that it will reach p′ or below at least once. In the region p′ ≧ p, P1 = 0. In the region p′ < p, P1 ≠ 0 and is furthermore a discontinuous function of p′ at every rational p′.

Keywords

BERNOULLI TRIALSSURVIVAL PROBABILITY DISCONTINUITYLATTICE RANDOM WALK
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 70 - 80
Copyright
Copyright © Applied Probability Trust 1988 

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Footnotes

Research supported in part by D.O.E. DE-AC02-76ER03077.

References

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