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| 研究生： |
謝松樺 Hsieh, Sung Hua |
|---|---|
| 論文名稱： |
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 |
| 指導教授： |
蔡紋琦
Tsai, Wen Chi |
| 學位類別： |
碩士
Master |
| 系所名稱： |
商學院 - 統計學系 Department of Statistics |
| 論文出版年： | 2009 |
| 畢業學年度： | 97 |
| 語文別： | 中文 |
| 論文頁數： | 71 |
| 中文關鍵詞： | 字串 、等候時間 、馬可夫鏈 |
| 外文關鍵詞： | string, waiting time, markov chain |
| 相關次數： | 點閱：192 下載：0 |
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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.
第一章 緒論..............................................1
第一節 符號介紹......................................1
第二節 文獻回顧......................................2
第三節 問題介紹......................................4
第二章 電腦計算結果......................................6
第一節 字串長度為3的後選優勢探討....................6
第二節 字串長度為4,5,6的後選優勢探討................9
第三章 失敗的策略.......................................11
第四章 主要定理........................................ 17
第一節 為 時的隊伍二後選優勢................17
第二節 為 時的隊伍二後選優勢............52
第三節 隊伍二必不敗的策略...........................55
第五章 結論.............................................58
附錄.....................................................60
參考文獻.................................................70
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