English

Spacing Distribution of a Bernoulli Sampled Sequence

Probability 2015-10-14 v1

Abstract

We investigate the spacing distribution of sequence Sn={0,1n,2n,,n1n,1}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.

Keywords

Cite

@article{arxiv.1510.03500,
  title  = {Spacing Distribution of a Bernoulli Sampled Sequence},
  author = {Abigail L. Turner and Ananya Uppal and Peng Xu},
  journal= {arXiv preprint arXiv:1510.03500},
  year   = {2015}
}
R2 v1 2026-06-22T11:18:40.252Z