| URN |
etd-0719106-131107 |
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| Author |
Chia-Hui Lin |
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| Author's Email Address |
m932040004@student.nsysu.edu.tw |
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| Statistics |
This thesis had been viewed 5180 times. Download 1721 times. |
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| Department |
Applied Mathematics |
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| Year |
2005 |
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| Semester |
2 |
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| Degree |
Master |
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| Type of Document |
|
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| Language |
English |
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| Title |
A STUDY OF SHUFFLING CARDS AND STOPPING TIMES FOR RANDOMNESS |
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| Date of Defense |
2006-06-16 |
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| Page Count |
24 |
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| Keyword |
randomness
goodness of fit test
shuffle times
simulation
|
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| Abstract |
In this paper we analyze how many shuffles are necessary to get close to ran- domness for a deck of n cards. Aldous (1983) shows that approximately 8.55 (n=52) shuffles are necessary when n is large. Bayer and Diaconis (1992) use the variation distance as a measure of randomness to analyze the most commonly used method of shuffling cards, and claim that 7 shuffles are enough when n=52. We provide another idea to measure the distance from randomness for repeated shuffles. The proposed method consists of a goodness of fit test and a simple simulation. Simulation results show that we have a similar conclusion to that of Bayer and Diaconis. |
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| Advisory Committee |
Fu-Chuen Chang - chair
Mong-Na Lo Huang - co-chair
Mei-Hui Guo - co-chair
Chin-San Lee - advisor
|
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| Files |
indicate in-campus access immediately and off_campus access in a year |
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| Date of Submission |
2006-07-19 |
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