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研究生: 莊孟霏
CHUANG, MENG-FEI
論文名稱: 秘書問題與其新型推廣
The Secretary Problem and Its New Variation
指導教授: 胡殿中
HU, TIEN-CHUNG
口試委員: 趙一峰
呂理裕
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系
Department of Mathematics
論文出版年: 2016
畢業學年度: 104
語文別: 中文
論文頁數: 52
中文關鍵詞: 秘書問題
外文關鍵詞: The Secretary Problem
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  • 本文第二章介紹了四個版本的秘書問題,並且在第三章作變化,研究新型的秘書問題。
    在原始版本的秘書問題情境下,增設了錄取門檻-及格分數的限制,未達及格分數者,不予以錄取。已知不及格人數共有𝑡位,我們目標是最大化選中實際第一名的機率。


    In Chapter 2, we introduce four versions of the secretary problem, and make its new variation in Chapter 3.

    We add the “threshold value” (or “passing score”) into the situation of the standard secretary problem, and the one whose scores are below this value would not be admitted. Given t, the total number of people who fail, we hope to find the maximum probability of selecting the best person.

    第 1 章 前言 1.1. 研究動機 1 1.2. Backward Induction 3 第2 章 秘書問題 2.1. 最大化錄取實際第一名的機率 6 2.2. 最佳化被錄取者名次的平均值 15 2.3. 最大化錄取實際第一名或實際第二名的機率 26 2.4. 分組,並最大化錄取實際第一名的機率 31 第3 章 秘書問題的新版變形 3.1. 增設及格分數的限制 37 3.2. 與原始版本的秘書問題作比較 46 第4 章 結語 4.1. 回顧 48 4.2. 展望-Backward Induction 在骰子遊戲上的應用 49 參考文獻 52

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