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    A note on the closed-form solution for the longest head run problem of Abraham de Moivre

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    2009.07765.pdf (105.3Kb)
    Links to Files
    https://arxiv.org/abs/2009.07765
    Permanent Link
    http://hdl.handle.net/11603/20080
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    • UMBC Faculty Collection
    • UMBC Mathematics and Statistics Department
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    Author/Creator
    Malinovsky, Yaakov
    Date
    2020-09-16
    Type of Work
    6 pages
    Text
    journal articles preprints
    Citation of Original Publication
    Malinovsky, Yaakov; A note on the closed-form solution for the longest head run problem of Abraham de Moivre; History and Overview (2020); https://arxiv.org/abs/2009.07765
    Rights
    This item is likely protected under Title 17 of the U.S. Copyright Law. Unless on a Creative Commons license, for uses protected by Copyright Law, contact the copyright holder or the author.
    Abstract
    The problem of the longest head run was introduced and solved by Abraham de Moivre in the second edition of his book Doctrine of Chances (de Moivre, 1738). The closed-form solution as a finite sum involving binomial coefficients was provided in Uspensky (1937). Since then, the problem and its variations and extensions have found broad interest and diverse applications. Surprisingly, a very simple closed form can be obtained, which we present in this note.


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    Albin O. Kuhn Library & Gallery
    University of Maryland, Baltimore County
    1000 Hilltop Circle
    Baltimore, MD 21250
    www.umbc.edu/scholarworks

    Contact information:
    Email: scholarworks-group@umbc.edu
    Phone: 410-455-3021


    If you wish to submit a copyright complaint or withdrawal request, please email mdsoar-help@umd.edu.