高尔顿板实验动态演示

1、 / 7高尔顿板实验动态演示篇一 : 高尔顿钉板试验模拟（ 程序 ） 高尔顿钉板试验模拟（程序）. 这是我 2005年 12的课程设计中程序的核心部分，写完后自己非常得意，等着老师表扬。等啊等，等待现在也没等到:em16:现将它献给大家（若有版权那遵守BSDAE）注1:程序以前是用Matlab 写的现用Java 重写注2：原程序中galton 返回值为int grid 、没有“输出结果”部分public void galton（int sumOfGrid, intsumOfBall） int grid = new intsumOfGrid;int number = 0;/ 一个小球从顶端落下过

2、程中向右偏移的总次数int rand ;/ 随机数，取值范围为0,1 ，为 0、为 1 的概率相等for( int counter_ball = 1; counter_ball/ (sumOfGrid - 1) 为钉板的层数for( int times = 1; times gridnumber+; number = 0; TOC o 1-5 h z / 输出结果System.out.println( 小球的总数为+sumOfBall+t 格子的个数为 +sumOfGrid );for( int index = 0; index System.out.println( (index+1)+号格

3、子中的小球数为：t+gridindex );/end of metod galton补充： ( 谢谢 2 楼提醒 :-D )高尔顿钉板试验：自板上端放入一小球, 任其自由落下. 在下落过程中 , 当小球碰到钉子时, 从左边落下与从右边落下的机会相等. 碰到下一排钉子也是如此. 自板上端放入n（n 自行输入 ） 个小球 , 观察小球落下后呈现曲线并统计小球落入各个格子的频率.高尔顿钉板试验可见概率论（复旦大学李贤平）当小球数量少时分布无明显特征，当小球数量多时（100）分布近似正态分布。（即两边对称:-D ） 当时为了证明服从正态分布投1 千万个小球（计算机模拟:-D ）Galton Board

4、The Galton board, also known as a quincunx or bean machine, is a device for statistical experiments named after English scientist Sir Francis Galton. It consists of an upright board with evenly spaced nails （or pegs） driven into its upper half, where the nails are arranged in staggered order, and a

5、lower half divided into a number of evenly-spaced rectangular slots. The front of the device is covered with a glass cover to allowviewing of both nails and slots. In the middle of the upper edge, there is a funnel into which balls can be poured, where the diameter of the balls must be much smaller

6、than the distancebetween the nails. The funnel is located precisely above the central nail of the second row so that each ball, if perfectly centered, would fall vertically and directly onto the uppermost point of this nails surface (Kozlov and Mitrofanova 2002). The figure above shows a variant of

7、the board in which only the nails that can potentially be hit by a ball dropped from the funnel are included, leading to a triangular array instead of a rectangular one.Each time a ball hits one of the nails, it can bounce right (or left) with someprobabilityp(and q1p). For symmetricallyplaced nails

8、, balls will bounce left or right with equal probability, so p q 1/2. If the rows are numbered from 0 to N 1, he path of each falling ball is a Bernoulli trial consisting ofNsteps. Each ball crosses the bottom row hitting the nth peg from the left (where。 n N 1) if it has taken exactly right turns,

9、which occurs with probabilityThis process therefore gives rise to a binomial distribution of in the heights of heaps of balls in the lower slots.If the number of balls is sufficiently large and, then according to the weak law of large numbers, the distribution of the heights of the ball heaps will a

10、pproximate a normaldistribution.Somecare is needed to obtain these idealized results, however, as the actual distribution of balls depends on physicalproperties of the setup, including the elasticity of the balls(as characterized by their coefficient of restitution), theradius of the nails, and the

11、offsets of the balls over thefunnels opening whenthey are dropped (Kozlov and Mitrofanova 2002). 高尔顿板实验动态演示篇二：高尔顿钉板R语言实验高尔顿钉板试验【实验目的】1、加强对正态分布的理解2、了解独立同分布的中心极限定理3、掌握R在计算机模拟中的应用【实验要求】1、了解R 程序文件的建立和运行，理解循环等控制语句的应用。2、了解R的程序设计，掌握用R处理实际问题的能力。【实验内容】高尔顿钉板试验，这个试验是英国科学家高尔顿设计的，具体如下：自板上端放一个小球，任其自由下落。在其下落过程中，当小球碰到钉子时从左边落下的概率为p,从右边落下的概率为1-p,碰到下一排钉子又是如此，最后落到底板中的某一格子，因此任意放入一球，则此球落入哪个格子事先难以确定（设横排共有m=20非钉子，每一排钉子等距排列，下一排每个钉子恰好在上一排两相邻钉子中间）。（ 1） 分别取 p=0.1