基于固定问题对贝特朗奇论的理论和随机模拟研究  

Theoretical analysis and stochastic simulation of Bertrand Paradox on the basis of the fixed problems

作　　者：李姣娜[1] LI Jiao-na(General Education and International College,Chongqing College of Electronic Engineering,Chongqing 401331,China)

机构地区：[1]重庆电子工程职业学院通识教育与国际学院,重庆401331

出　　处：《宝鸡文理学院学报（自然科学版）》2019年第1期12-15,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：目的对"贝特朗奇论"常规解法中的关键条件(固定弦的端点或弦的方向)推广为随机取点或弦的方向。方法从连续型随机变量的密度函数入手给出概率值的理论计算,借助Matlab软件编程,进行蒙特卡罗随机模拟试验。结果与结论多角度地探讨了常规解法中的固定端点和固定弦的方向问题,肯定了常规解法的正确性,同时也得到"固定与否"不影响事件的概率值。Purposes- To generalize the key conditions for the general solutions of the Bertrand's question to stochastic points or the direction of chords. Methods- The theoretical probability value of theoretical calculation is given by the density function of continuous random variables.With the help of the computer,Matlab software programming and Monte Carlo method were used to simulation. Result and Conclusion- The correctness of the general solutions were affirmed by discussing the directional problems of fixed endpoints and fixed chords in the general solutions,both theoretical and practical methods show that "fixedation" does not affect the probability value.

关 键 词：贝特朗奇论 密度函数 几何概率 随机模拟 概率 

分 类 号：O211.1[理学—概率论与数理统计]