Words in Random Binary Sequences I

Words in Random Binary Sequences I

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 \(W\) a...

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Veröffentlicht in:arXiv.org 2021-07
Hauptverfasser: Ennis, Christian, Holland, William, Mujawar, Omer, Narayanan, Aadit, Neubrander, Frank, Neubrander, Marie, Simino, Christina
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creator Ennis, Christian
Holland, William
Mujawar, Omer
Narayanan, Aadit
Neubrander, Frank
Neubrander, Marie
Simino, Christina
description 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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