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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 P 1 that this estimate always lies above some pre-selected rational fraction p′, and its complement P 2, the probability that it will reach p′ or below at least once. In the region p′ ≧ p, P 1 = 0. In the region p′ < p, P 1 ≠ 0 and is furthermore a discontinuous function of p′ at every rational p′.

Keywords

BERNOULLI TRIALSSURVIVAL PROBABILITY DISCONTINUITYLATTICE RANDOM WALK

Information

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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