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中文题名:

 “三门问题”探究    

姓名:

 刘璐    

保密级别:

 公开    

论文语种:

 中文    

学科代码:

 070101    

学科专业:

 数学与应用数学    

学生类型:

 学士    

学位:

 理学学士    

学位年度:

 2018    

学校:

 北京师范大学    

校区:

 北京校区培养    

学院:

 数学科学学院    

第一导师姓名:

 李勇    

第一导师单位:

 北京师范大学统计学院    

提交日期:

 2018-05-24    

答辩日期:

 2018-05-16    

外文题名:

 Study on Monty Hall Problem    

中文关键词:

 “三门问题” ; 主持人开门规则 ; 条件概率 ; 问题情境刻画    

中文摘要:
本文主要介绍了著名概率问题“三门问题”的由来以及此问题存在的两种争论,基于争论双方都认同的问题刻画条件,针对其表述中含糊的地方,本文加入主持人行为的假设,得到在这些刻画条件之下换门和不换门赢得汽车的概率与主持人开门的规则有关,并通过计算机模拟对推导结论加以验证。主流条件概率推导中忽略了“游戏参与者初始选择一号门”这一前提,本文指出了这一错误并加以修正,结合主持人不同开门规则下得到的结论,可以得到主流观点和直观结论之间并不矛盾,两种是问题背景下主持人按照不同规则打开山羊门的两种结果,引发“三门问题”争论的原因在于争论双方认为自己所添加的假设自然成立。本文还对问题背景中汽车放置规律进行了讨论,得到“三门问题”最一般情形下的概率表达式和决策方式。结合全文对“三门问题”的探究,本文最后强调了实际问题数学刻画的重要性并提出了关于此类问题的几点思考。
外文摘要:
This article mainly introduces the famous probability problem, Monty Hall problem. There are two arguments on this problem in the process of its origin and development. Based on the problem description common to both sides, the article discusses the influence of different open-door rules related to the host. The conclusion is that the probability of winning the car whether by switching the door or not is connected to the host’s behavior and rules,which is verified by computer simulation in the article. The known condition that the game player chose door 1 initially is ignored in mainstream derivation basing on conditional probability. This error is pointed out and corrected in this article. In fact, there is no contradiction between the two arguments, which are two outcomes in different situation depending on the hosts’ open-door rules. In addition, the rules how the car is placed are discussed and the formula for the most general case is derived. Suggestions when coming across problems under actual situation are put forward at the end of this article.
参考文献总数:

 10    

插图总数:

 0    

插表总数:

 1    

馆藏号:

 本070101/18089    

开放日期:

 2019-07-09    

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