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| Title: | 依序選擇四字串使第二字串或第四字串先出現的後選優勢探討
On the first occurrence of four strings with teams |
| Authors: | 謝松樺
Hsieh, Sung Hua |
| Contributors: | 蔡紋琦
Tsai, Wen Chi
謝松樺
Hsieh, Sung Hua |
| Keywords: | 字串
等候時間
馬可夫鏈
string
waiting time
markov chain |
| Date: | 2008 |
| Issue Date: | 2009-09-14 |
| Abstract: | 本論文主要是在探討依序選擇四個字串之下，是否存在一策略使得第二或第四字串有較大的機會比第一或第三字串先出現，也就是所謂的後選優勢是否存在。
利用電腦計算，我們發現字串長度為4,5,6時後選優勢確實存在，而當字串長度大於等於或等於7時，我們則證明了若第一字串為(0,0,...,0),(0,0,...,0,1),(1,1,...,1)或(1,1,...,1,0)時，後選者優勢亦存在。
In the thesis, we consider about the first occurrence of four strings decided sequentially with teams. Team 1 consists string 1 and string 3; team 2 consists string 2 and string 4. It is interested in whether or not team 2 whose strings are decided after first string and third string are given separately gets an advantage in appearing with larger probability.Namely, given any string 1, we want to find a string 2 such that any string 3 corresponds to at least one string (string 4) making
a larger probability for team 2 in appearing earlier than team 1.
Based on the result from computer calculation, team 2 advantage over team 1 when the string length is 4, 5, and 6. This thesis also shows that team 2 gets an advantage for cases where string 1 is (0,0,...,0), (0,0,...,0,1), (1,1,...,1), (1,1,...,1,0) ,when the string length is
larger than 6. |
| Reference: | [1]Chen, R. (1989) A circular property of the occurrence of sequence patterns in the fair coin-tossing process, Adv. Appl. Probability,
Vol.21, pp.938-940.
[2]Chen, R. and Lin, H.E. (1984) On fair coin toissing process, J.
Multivariate Anal., Vol15, pp.222-227.
[3]Chen, R. and Zame, A. (1979) On fair coin-toissing game, J.
Multivariate Anal., Vol9, pp.150-157.
[4]Chen, R., Hung, Y.-C., Chen M.-R.and Zame, A.,On the first occurrence of complement strings (unpublished).
[5]Chen, R., Rosenberg, B. and Zame, A. (1979) On the first occurrence of strings, (unpublished).
[6]Gerber, H. V. and Li, S.Y.R. (1981) The occurrence of sequence patterns in repeated experiments and hitting times in a Markov chain, Stoch.
Process and Their Application, Vol.11, pp.101-108.
[7]Guibs,L. and Odlyko, A. M. (1981) String overlaps, pattern matching, and nontransitive games.,J. Combin. Theory Ser.A, Vol.30, pp.1183-208.
[8]Li, S. Y. R. (1980) A martingale approach to the study of occurrence of sequence patterns in repeated experiments ,Annals of Probability,
Vol.8, pp.1171-1176.
[9]Pozdnyakov, V. (2008) On occurrence of patterns in markov chains: Method of gambling teams, Stat. & Prob. Letters, Vol.78, Pages2559-2838.
[10]Williams, D. (1991) Probability with Martingales, Cambridge University Press, Cambridge. |
| Description: | 碩士
國立政治大學
統計研究所
96354018
97 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0096354018 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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