2015•arXiv (Cornell University)Open access

Spacing Distribution of a Bernoulli Sampled Sequence

Abigail L. Turner, Ananya Uppal, Peng Xu

Abstract

We investigate the spacing distribution of sequence \[S_n=\left\{0,\frac{1}{n},\frac{2}{n},\dots,\frac{n-1}{n},1\right\}\] after Bernoulli sampling. We describe the closed form expression of the probability mass function of the spacings, and show that the spacings converge in distribution to a geometric random variable.

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Key concepts: Bernoulli's principle, Bernoulli distribution, Sequence (biology), Random variable, Combinatorics, Distribution (mathematics), Mathematics, Function (biology)