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## The Number of Consecutive Heads in a Run

File
Title
The Number of Consecutive Heads in a Run
Author
氏名 Hirose Hideo ヒロセ ヒデオ 廣瀬 英雄
Subject
coin tossing
run
dual problem
Abstract

How many consecutive heads do we observe in a run of coin tossing of length n? Although the problem seems to be easy to answer, this would be actually a little bit tough when we try to prove it straightforwardly. The expected number of consecutive heads in a run is 3n-2/8 (n≧2) using the recursive formula.

However, if we define a solitary head coin such that a head coin is isolated by neighboring tail coin(s) in a run, the problem of how many solitary heads we observe in a run can be solved easily. The expected number of solitary heads in a run is n+2/8 (n≧2). Since the problem of solitary head coin becomes a dual problem of the above, the consequence of the problem of the consecutive heads is derived easily by considering the probability of a solitary coin appearance.

Journal Title

Volume
53
Spage
177
Epage
179
Published Date
2019-02
Publisher

ISSN
1346-9975
NCID
AA11599110
Language
eng
NIIType
Departmental Bulletin Paper
Text Version

Rights
publisher
Set
it-hiroshima