/* S0310.java
 *       ベルヌーイ試行のシミュレーション 
 *         (C) H.Ishikawa 2008 
 */

package simulation;
import java.applet.*;
import java.awt.*;
import java.text.*;

public class S0310 extends Applet{

	public void paint(Graphics g) {
		int  M = 1000000;              /*発生させる乱数の数*/
		int    j;                      /* forのカウンタ */
		int    k;                      /* 表の出た回数 */
		int    n = 6;                  /* コイン投げの回数 */
		int    b[] = new int [20];    /* 度数 */
		double p = 0.5;                /* 表の出る確率 */
		double binom;                  /* 理論値 */
		DecimalFormat exFormat1 = new DecimalFormat(" 0.000000");

		for (j = 1; j <= M; j ++) {
			k = bernoulli(p, n);
			b[k] = b[k] + 1;
		}
  
		
		
		g.drawString("      k        simulation          theory", 10, 10);
		
		for (k = 0; k <= n; k ++) {
			binom = (double) b[k] / M;
			g.drawString("     " + k, 10 , 20 + 10 * k);
			g.drawString("     " + exFormat1.format(binom), 40 , 20 + 10 * k);
			g.drawString("     " + exFormat1.format(binomial(p, n, k)), 120 , 20 + 10 * k);
		}
	}

	public static int bernoulli(double p, int n){
		int k, i;
		k = 0;
		for (i = 1; i <= n; i++) {
			if (p > Math.random()) {
				k = k + 1;
			}
		}
		return (k);
	}

	public static double binomial(double p, int n, int k){
		int i;
		int k1 = 1;
		int n1 = 1;
		double b;
		for (i = 1; i <= k; i ++) {
			k1 = k1 * i;
		}
		for (i = n - k + 1; i <= n; i++) {
			n1 = n1 * i;
		}
		b = (double)n1 / k1 *  Math.pow(p,(double)k) *  Math.pow((1 - p), (double)(n - k));
		return (b);
	}

}