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1 results

  • On the Random Sampling of Pairs, with Pedestrian Examples

  • Part of
  • Richard Arratia, Stephen DeSalvo
  • Journal:
    Advances in Applied Probability / Volume 47 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    04 January 2016, pp. 292-305
    Print publication:
    March 2015
    • Article
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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.