The Number of Consecutive Heads in a Run
URI | http://harp.lib.hiroshima-u.ac.jp/it-hiroshima/metadata/12289 | ||||||
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research53_177-179.pdf
( 521.0 KB )
Open Date
:2019-02-15
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Title |
The Number of Consecutive Heads in a Run
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Author |
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Subject |
coin tossing
run
consecutive heads
solitary head coin
dual problem
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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. |
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Journal Title |
広島工業大学紀要. 研究編
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Volume |
53
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Spage |
177
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Epage |
179
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Published Date |
2019-02
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Publisher |
広島工業大学
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ISSN |
1346-9975
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NCID |
AA11599110
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Language |
eng
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NIIType |
Departmental Bulletin Paper
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Text Version |
出版社版
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Rights |
publisher
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Set |
it-hiroshima
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