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On the probability of forming polygons from a broken stick

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  • Verreault, William

Abstract

Break a stick at random at n−1 points to obtain n pieces. We give an explicit formula for the probability that every choice of k segments from this broken stick can form a k-gon, generalizing similar work. The method we use can be applied to other geometric probability problems involving broken sticks, which are part of a long-standing class of recreational probability problems with several applications to real-world models.

Suggested Citation

  • Verreault, William, 2022. "On the probability of forming polygons from a broken stick," Statistics & Probability Letters, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:stapro:v:180:y:2022:i:c:s0167715221001991
    DOI: 10.1016/j.spl.2021.109237
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    References listed on IDEAS

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    1. F. W. Steutel, 1967. "Random division of an interval," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 21(3‐4), pages 231-244, September.
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