The Number of Consecutive Heads in a Run

URI http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/12289
ファイル
タイトル
The Number of Consecutive Heads in a Run
著者
氏名 Hirose Hideo
ヨミ ヒロセ ヒデオ
別名 廣瀬 英雄
キーワード
coin tossing
run
consecutive heads
solitary head coin
dual problem
抄録

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.

掲載雑誌名
広島工業大学紀要. 研究編
53
開始ページ
177
終了ページ
179
出版年月日
2019-02
出版者
広島工業大学
ISSN
1346-9975
NCID
AA11599110
本文言語
英語
資料タイプ
紀要論文
著者版フラグ
出版社版
権利情報
publisher
区分
it-hiroshima