记录一下最近的数学作业：
超几何分布定义：
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代码实现：

因为是离散型随机变量，所以顺次计算出每种情况的概率，再随机生成10000个0-1之间的随机数（用于模拟概率），然后用这些生成的概率去比对他们应该落入的区间，最后逐个累加，统计频率，然后用频率/10000去计算概率，最后绘制2条曲线，1条是理论，1条是模拟。

package test;import org.jfree.chart.ChartFactory;
import org.jfree.chart.ChartFrame;
import org.jfree.chart.JFreeChart;
import org.jfree.chart.plot.CategoryPlot;
import org.jfree.chart.plot.PlotOrientation;
import org.jfree.data.category.DefaultCategoryDataset;import java.awt.*;
import java.text.DecimalFormat;
import java.util.Scanner;public class Cjhfb {private static double[] rn;//随机数private int n;//摸球总数private int m;//黑色球总数private int z;//球的总数public Cjhfb() {this.rn = randomNum();}//求概率 返回数组public double[] Probability() {double[] prob = new double[10000];for (int i = 0; i <= n; i++) {double temp = (double) (combination(i, m)) * (double) (combination(n - i, z - m)) /(double) (combination(n, z));String result = String.format("%.6f", temp);prob[i] = Double.parseDouble(result);}return prob;}//计算累计概率public double[] cumulativeProbability() {double[] probability = Probability();double[] cumulativeprobability = new double[10000];int k = 0;for (int i = 0; i <= n; i++) {double temp = 0;for (int j = 0; j <= i; j++) {temp += probability[j];}cumulativeprobability[k++] = temp;}return cumulativeprobability;}//计算频率public int[] frequency() {int[] freq = new int[n + 1];for (int i = 0; i < n + 1; i++) {freq[i] = 0; //初始化数组为0}double[] rnum = randomNum();double[] cpro = cumulativeProbability();for (int i = 0; i < 10000; i++) {for (int j = 0; j < n + 1; j++) {if (rnum[i] < cpro[j]) {freq[j]++;break;}}}return freq;}//计算生成的频率对应的概率public double[] frequencyProbability() {double frequencyprobability[] = new double[n + 1];int[] freq = frequency();for (int i = 0; i < n + 1; i++) {frequencyprobability[i] = (double) freq[i] / 10000;}return frequencyprobability;}//求期望public double expectation() {return (double) n * (double) m / (double) z;}//求方差public double variance() {double n1 = (double) n;double m1 = (double) m;double z1 = (double) z;return (n1 * m1 * (z1 - m1) * (z1 - n1)) / (z1 * z1 * (z1 - 1));}//生成随机数public static double[] randomNum() {double[] rn = new double[10000];for (int i = 0; i < 10000; i++) {double a = Math.random();DecimalFormat two = new DecimalFormat("#.000000");//"0.00"String str = two.format(a);rn[i] = Double.parseDouble(str);}return rn;}//求阶乘public static long factorial(int x) {long sum = 1;while (x > 0) {sum = sum * x--;}return sum;}//求组合public static long combination(int m, int n) {if (m > n)return 0;if (m == n || m == 0) return 1;if (m > n / 2) {m = n - m;}return factorial(n) / (factorial(m) * factorial(n - m));}//卡方检验public static double KF_Check(double[] arr/*理论值*/, double[] brr/*实际值*/, int n) {double ret = 0;for (int i = 0; i < n + 1; i++) {double temp = ((arr[i] - brr[i]) * (arr[i] - brr[i])) / brr[i];ret += temp;}return ret;}public static void main(String[] args) {Scanner input = new Scanner(System.in);System.out.println("请输入样本总数N");Cjhfb cjhfb = new Cjhfb();cjhfb.z = input.nextInt();System.out.println("请输入指定样本数量M");int x0 = input.nextInt();cjhfb.m = x0;System.out.println("请输入抽样个数n");int x = input.nextInt();cjhfb.n = x;if (x0 < x) x = x0;System.out.println("---------------------期望-------------------------");System.out.println(cjhfb.expectation());System.out.println("---------------------方差-------------------------");System.out.println(cjhfb.variance());System.out.println("---------------------概率-------------------------");double[] probs = cjhfb.Probability();for (int i = 0; i <= x; i++) {System.out.println("X="+i+": "+probs[i]);}System.out.println("--------------------累计概率----------------------");double[] cumulativeProbability = cjhfb.cumulativeProbability();for (int i = 0; i <= x; i++) {System.out.println(cumulativeProbability[i]);}System.out.println("----------------------频率------------------------");int[] freq = cjhfb.frequency();for (int i = 0; i <= x; i++) {System.out.println("X="+i+":的频率："+freq[i]+" 对应的概率："+cjhfb.frequencyProbability()[i]);}System.out.println("----------卡方检验，自由度为" + x + "，进而查表------------");System.out.println(cjhfb.KF_Check(cjhfb.frequencyProbability(), probs, x));DefaultCategoryDataset dataset = new DefaultCategoryDataset();//创建数据集对象for (int i = 0; i <= x; i++) {dataset.addValue(probs[i],""+i,""+i);//数据值，X轴，Y轴}JFreeChart mchart = ChartFactory.createBarChart("bar chart","X",//横坐标1"probability", //纵坐标dataset,//数据集PlotOrientation.VERTICAL,true,//显示图例true,//采用标准生成器false//是否生成超链接);CategoryPlot mplot = (CategoryPlot) mchart.getPlot();mplot.setBackgroundPaint(Color.lightGray);mplot.setRangeGridlinePaint(Color.orange);//背景底部横虚线mplot.setOutlinePaint(Color.green);//边界线ChartFrame mchartframe = new ChartFrame("超几何分布", mchart);mchartframe.pack();mchartframe.setVisible(true);}
}