Distributions of periods and frequencies of runs in random binary sequences
type: Item
instance of: scholarly article
title: Distributions of periods and frequencies of runs in random binary sequences
zbMATH Open document ID: 0702.60013
DOI: 10.1016/0196-8858(89)90015-8
published in: Advances in Applied Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The paper concerns random binary sequences in which 1's and 0's occur independently, with respective probabilities p and \(q=1-p\). As the main result it is shown that the probabilities p(k) that the length of the interval from the beginning of one run of 1's to the next is exactly k units, is equal to \((p^ kq-q^ kp)/(p-q)\) for \(p\neq q\) and \((k- 1)2^{-k}\) if \(p=q=1/2\). This result seems to be well-known for a long time. It could be a good exercise for students in a first course of probability.
Mathematics Subject Classification ID: 60C05
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60F99
zbMATH DE Number: 4151502
zbMATH Keywords: periods and frequencies of runs
zbMATH Keywords: generating function
zbMATH Keywords: random binary sequences
author: S. W. Golomb
reviewed by: Lothar Heinrich
MaRDI profile type: Publication
full work available at URL: 0196-8858(89)90015-8
OpenAlex ID: W1974015498
cites work: Q5798359
cites work: Q3284008
cites work: Sources which maximize the choice of a Huffman coding tree
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description: scientific article; zbMATH DE number 4151502