The Number of Consecutive Heads in a Run

URI http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/12289
File
Title
The Number of Consecutive Heads in a Run
Author
氏名 Hirose Hideo
ヨミ ヒロセ ヒデオ
別名 廣瀬 英雄
Subject
coin tossing
run
consecutive heads
solitary head coin
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
広島工業大学紀要. 研究編
Volume
53
Spage
177
Epage
179
Published Date
2019-02
Publisher
広島工業大学
ISSN
1346-9975
NCID
AA11599110
Language
eng
NIIType
Departmental Bulletin Paper
Text Version
出版社版
Rights
publisher
Set
it-hiroshima