On long runs of heads and tails
type: Item
instance of: scholarly article
title: On long runs of heads and tails
zbMATH Open document ID: 0796.60033
DOI: 10.1016/0167-7152(94)90137-6
author: Tamás F. Móri
published in: Statistics \& Probability Letters
publication date: 1994-09-20T00:00:00Z
review text: In fair coin tossing, i.e. for an i.i.d. sequence of Bernoulli random variables with values \(H\) (head) and \(T\) (tail), both occurring with probability \(1/2\), let \(Z_ H(n)\) and \(Z_ T(n)\) denote the length of the longest head resp. tail run observed during the first \(n\) tosses. It is shown that the logarithmic density of the random sequence of those \(n\) for which the difference \(Z_ H(n)-Z_ T(n)\) falls into a fixed subset of the set of all integers exists with probability one, and the value of this density is given explicitly.
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 503650
zbMATH Keywords: logarithmic density
zbMATH Keywords: almost sure limit distribution
zbMATH Keywords: fair coin tossing
MaRDI profile type: Publication
full work available at URL: 0167-7152(94)90137-6
OpenAlex ID: W2082098006
cites work: Q4035984
cites work: Q4136276
cites work: Q3766608
cites work: An extreme value theory for long head runs
cites work: Long repetitive patterns in random sequences
cites work: The A.S. Limit Distribution of the Longest Head Run
cites work: Q4277402
cites work: Asymptotic independence of 'pure head' stopping times
cites work: Q3998747
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description: scientific article; zbMATH DE number 503650