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Words in Random Binary Sequences I (2107.01029v1)
Published 1 Jul 2021 in math.GM
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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