Advances in Applied Probability

On the random sampling of pairs, with pedestrian examples

Richard Arratia and Stephen DeSalvo

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Abstract

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.

Article information

Source
Adv. in Appl. Probab., Volume 47, Number 1 (2015), 292-305.

Dates
First available in Project Euclid: 31 March 2015

Permanent link to this document
https://projecteuclid.org/euclid.aap/1427814592

Digital Object Identifier
doi:10.1239/aap/1427814592

Mathematical Reviews number (MathSciNet)
MR3327326

Zentralblatt MATH identifier
1312.65007

Subjects
Primary: 65C50: Other computational problems in probability
Secondary: 60C05: Combinatorial probability

Keywords
Total variation distance random sampling computational algebraic geometry Poisson process pair-derived distribution

Citation

Arratia, Richard; DeSalvo, Stephen. On the random sampling of pairs, with pedestrian examples. Adv. in Appl. Probab. 47 (2015), no. 1, 292--305. doi:10.1239/aap/1427814592. https://projecteuclid.org/euclid.aap/1427814592


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References

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