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On the Random Sampling of Pairs, with Pedestrian Examples

Part of: Probabilistic methods, simulation and stochastic differential equations Combinatorial probability

Published online by Cambridge University Press:  04 January 2016

Richard Arratia  and
Stephen DeSalvo
Richard Arratia*
Affiliation:
University of Southern California
Stephen DeSalvo*
Affiliation:
University of California, Los Angeles
*
∗ Postal address: Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA.
∗∗ Postal address: Department of Mathematics, University of California, Los Angeles, CA 90095, USA. Email address: [email protected]
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Abstract

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For a collection of objects such as socks, which can be matched according to a characteristic such as color, we study the innocent phrase ‘the distribution of the color of a matching pair’ by looking at two methods for selecting socks. One method is memoryless and effectively samples socks with replacement, while the other samples socks sequentially, with memory, until the same color has been seen twice. We prove that these two methods yield the same distribution on colors if and only if the initial distribution of colors is a uniform distribution. We conjecture a nontrivial maximum value for the total variation distance of these distributions in all other cases.

Keywords

Total variation distancerandom samplingcomputational algebraic geometryPoisson processpair-derived distribution

MSC classification

Primary: 65C50: Other computational problems in probability
Secondary: 60C05: Combinatorial probability
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 47 , Issue 1 , March 2015 , pp. 292 - 305
Copyright
© Applied Probability Trust 

References

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