Pick-up sticks problems for exponential and Pareto distributions
Matyas Barczy Rezső Lovas
作者信息
Abstract
We deal with the following two pick-up sticks problems: given an integer n greater than or equal to 3, we choose n sticks with independent random lengths from an exponential distribution or Pareto type I distribution, and we are interested in the probability that no three of them can be the sides of a triangle. In case of exponential distribution, this problem has been solved by other authors: the probability in question is equal to $n!/\big((F_3-1)(F_4-1)\cdots(F_{n+2}-1)\big)$, where $(F_i)_{i=1}^\infty$ is the sequence of Fibonacci numbers. We give a new, self-contained and detailed proof for this formula, which uses a different method compared to the earlier ones. In case of Pareto type I distribution, we derive new formulae for the corresponding probability.引用本文复制引用
Matyas Barczy,Rezső Lovas.Pick-up sticks problems for exponential and Pareto distributions[EB/OL].(2026-11-03)[2026-11-05].https://arxiv.org/abs/2611.04436.学科分类
数学
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