贝特朗奇论用计算机,用蒙特卡罗法求解贝特朗奇论.pdf-优快云博客

用蒙特卡罗法求解贝特朗奇论

理学院学报第12卷第4期 2013年4 月

JOURNAL OF DALI UNIVERSITY Vol.12 No.4 Apr. 2013

［DOI ］10. 3969 / j. issn. 1672-2345. 2013. 04. 004

用蒙特卡罗法求解贝特朗奇论

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段棂宴，凡彬，杨进，鹏程，刘绪涛

(1援内江师范学院数学与信息科学学院，四川内江 641100 ；

2援四川省高等学校数值仿真重点实验室，四川内江 641100)

［摘要］针对贝特朗奇所涉及的一个几何概率问题，由于3种不同样本空间的确定导致其结果的差异，利用蒙特卡罗法随机模

拟抽样来验证了解法3的合理性，借助计算机用Matlab软件编程以及数理统计中的统计计数等方法解决了该问题。不仅合理运

用了蒙特卡罗法原理，而且对理解以及进一步认识几何概率问题中的随机性具有重要意义。

［关键词］贝特朗奇；蒙特卡罗法；概率；统计

［中图分类号］O211.9 ［文献标志码］A ［文章编号］1672-2345(2013 )04-0009-03

Using the Monte Carlo Method to Solve the Bertrand Odd

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DUAN Lingyan ，WANG Fanbin ，YANG Jin ，WANG Pengcheng ，LIU Xutao

(1.College of Mathematics and Information Science ，Neijiang Normal University ，Neijiang, Sichuan 64 1100 ，China ；

2. Key Laboratory of Numerical Simulation in the Sichuan Province College ，Neijiang, Sichuan 64 1100，China )

〔Abstract 〕This paper is designed to solve the geometric probability problem of Bertrand paradox by using Monte Carlo method. Owing to

the result differences which are caused by three different samples space, Monte Carlo method is used to simulate random sampling to verify

the rationality of third method. And with the help of the computer, Matlab software programming and mathematical statistics in the

statistical counting method are used to solve this problem. This solution is not only using the Monte Carlo law principle reasonably, but also

important to understand and know more of the randomness of the geometric probability problem.

〔Key words 〕Bertrand odd theory ；Monte Carlo method ；probability ；sta

贝特朗奇论 用计算机,用蒙特卡罗法求解贝特朗奇论.pdf