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arXiv · 2107.01029

Words in Random Binary Sequences I

Christian Ennis·William Holland·Omer Mujawar·Aadit Narayanan·Frank Neubrander·Marie Neubrander·Christina Simino
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Abstract

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

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Christian Ennis, William Holland, Omer Mujawar, Aadit Narayanan, Frank Neubrander, Marie Neubrander, Christina Simino. 2021-07-01. Words in Random Binary Sequences I. https://arxiv.org/abs/2107.01029

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