English

Words in Random Binary Sequences I

General Mathematics 2021-07-05 v1

Abstract

When flipping a fair coin, let W=L1L2...LNW = L_1L_2...L_N with Li{H,T}L_i\in\{H,T\} be a binary word of length N=2N=2 or N=3N=3. In this paper, we establish second- and third-order linear recurrence relations and their generating functions to discuss the probabilities pW(n)p_{W}(n) that binary words WW appear for the first time after nn coin tosses.

Keywords

Cite

@article{arxiv.2107.01029,
  title  = {Words in Random Binary Sequences I},
  author = {Christian Ennis and William Holland and Omer Mujawar and Aadit Narayanan and Frank Neubrander and Marie Neubrander and Christina Simino},
  journal= {arXiv preprint arXiv:2107.01029},
  year   = {2021}
}