// CLTBernoulli.java // Written by Julian Devlin, 8/97, for the text book // "Introduction to Probability," by Charles M. Grinstead & J. Laurie Snell // Doesn't work for n > 400 import java.applet.Applet; import java.awt.*; public class CLTBernoulli extends java.applet.Applet { Float[] xSpikes; // Variables for simulation Float[] ySpikes; Float[] xLines; Float[] yLines; LineSpikeGraph lsg; // AWT elements Panel dispArea; Panel controls; // Panel for user controls Label numl1, numl2, numl3, numl4, numl5, numl6, numl7, numl8; // Controls TextField num1, num2, num3, num4; Button go; GridBagLayout gbl; GridBagConstraints cc; float mean, sigma; // Initialize applet public void init() { numl1 = new Label("n ="); // Create controls num1 = new TextField("100", 4); numl2 = new Label("p ="); // Create controls num2 = new TextField(".5", 4); numl3 = new Label("kmin ="); // Create controls num3 = new TextField("", 4); numl4 = new Label("kmax ="); // Create controls num4 = new TextField("", 4); numl5 = new Label("exact ="); numl6 = new Label(" "); numl7 = new Label("approx ="); numl8 = new Label(" "); go = new Button("Go"); lsg = new LineSpikeGraph(); // initialize a graphing space dispArea = new Panel(); // Set up window controls = new Panel(); setLayout(new BorderLayout(5, 5)); add("South", controls); add("Center", dispArea); dispArea.setLayout(new GridLayout(1, 1)); dispArea.add(lsg); gbl = new GridBagLayout(); controls.setLayout(gbl); cc = new GridBagConstraints(); cc.gridx = 0; cc.gridy = 0; gbl.setConstraints(numl1, cc); controls.add(numl1); cc.gridx = 1; gbl.setConstraints(num1, cc); controls.add(num1); cc.gridx = 2; gbl.setConstraints(numl2, cc); controls.add(numl2); cc.gridx = 3; gbl.setConstraints(num2, cc); controls.add(num2); cc.gridx = 0; cc.gridy = 1; gbl.setConstraints(numl3, cc); controls.add(numl3); cc.gridx = 1; gbl.setConstraints(num3, cc); controls.add(num3); cc.gridx = 2; gbl.setConstraints(numl4, cc); controls.add(numl4); cc.gridx = 3; gbl.setConstraints(num4, cc); controls.add(num4); cc.gridx = 0; cc.gridy = 2; gbl.setConstraints(numl5, cc); controls.add(numl5); cc.gridx = 1; gbl.setConstraints(numl6, cc); controls.add(numl6); cc.gridx = 2; gbl.setConstraints(numl7, cc); controls.add(numl7); cc.gridx = 3; gbl.setConstraints(numl8, cc); controls.add(numl8); cc.gridx = 0; cc.gridy = 3; cc.gridwidth = 4; gbl.setConstraints(go, cc); controls.add(go); validate(); } // Handle events public boolean handleEvent(Event evt) { String minStr, maxStr; if (evt.target instanceof Button) { if (evt.target == go && evt.id == Event.ACTION_EVENT) // When button is clicked { minStr = num3.getText().trim(); maxStr = num4.getText().trim(); if (minStr.length() != 0 && maxStr.length() != 0) simulate(Integer.valueOf(num1.getText()).intValue(), Float.valueOf(num2.getText()).floatValue(), Integer.valueOf(minStr).intValue(), Integer.valueOf(maxStr).intValue()); else if (minStr.length() != 0) simulate(Integer.valueOf(num1.getText()).intValue(), Float.valueOf(num2.getText()).floatValue(), Integer.valueOf(minStr).intValue(), Integer.valueOf(maxStr).intValue()); else simulate(Integer.valueOf(num1.getText()).intValue(), Float.valueOf(num2.getText()).floatValue()); return true; // Generate correct number of tosses } } return super.handleEvent(evt); // Handle other events as usual } public float normal(float x, float mu, float sigma) { return 1 / (sigma * (float) Math.pow(2 * Math.PI, .5)) * (float) Math.pow(Math.E, -1 * Math.pow(x - mu, 2) / (2 * Math.pow((double) sigma, 2))); } public float normalArea(float a, float b) { float mu = 0f; float sigma = 1f; int subdivisions = (int) Math.max(100, 20 * (double) Math.round( (double) b - (double) a + .5)); float dx = (b - a) / (float) subdivisions; float sum = normal(a, mu, sigma) + normal(b, mu, sigma); float x; for (int k = 1; k < subdivisions; k++) { x = a + (float) k * dx; if (k % 2 == 1) sum += 4 * normal(x, mu, sigma); else sum += 2 * normal(x, mu, sigma); } return dx / 3 * sum; } public void setPoints(int num, float prob) { float temp; mean = (float) num * prob; sigma = (float) Math.pow((double) ((float) num * prob * (1 - prob)), .5); float xmin = -4f; float xmax = 4f; float dx = (xmax - xmin) / 100f; int kmin = (int) Math.floor(Math.max(0, (double) (mean - 4 * sigma))) + 1; int kmax = (int) Math.ceil(Math.min((double) num, (double) (mean + 4 * sigma))) - 1; xLines = new Float[101]; yLines = new Float[101]; xSpikes = new Float[kmax - kmin + 1]; ySpikes = new Float[kmax - kmin + 1]; for (int k = kmin; k <= kmax; k++) { xSpikes[k - kmin] = new Float((k - mean) / sigma); temp = (float) Combinatorics.bernoulli(num, prob, k) * sigma; ySpikes[k - kmin] = new Float(temp); } for (int i = 0; i < 101; i++) { xLines[i] = new Float(xmin + i * dx); yLines[i] = new Float(normal(xmin + i * dx, 0f, 1f)); } } // Calculate probabilities public void simulate(int num, float prob) { setPoints(num, prob); dispArea.remove(lsg); lsg = new LineSpikeGraph(xLines, yLines, xSpikes, ySpikes); // Create new LineSpikeGraph dispArea.add(lsg); // Put up the graph validate(); } // Calculate probabilities public void simulate(int num, float prob, int min, int max) { setPoints(num, prob); dispArea.remove(lsg); lsg = new LineSpikeGraph(xLines, yLines, xSpikes, ySpikes, ((float) min - mean) / sigma, ((float) max - mean) / sigma); // Create new LineSpikeGraph dispArea.add(lsg); // Put up the graph if (min == max) { numl6.setText(String.valueOf(Combinatorics.bernoulli(num, prob, min))); numl8.setText(String.valueOf(normal((min - mean) / sigma, 0f, 1f) / sigma)); } else { float sum = 0; for (int k = min; k <= max; k++) { sum += Combinatorics.bernoulli(num, prob, k); } int flag = 1; numl6.setText(String.valueOf(sum)); numl8.setText(String.valueOf(normalArea((min - mean) / sigma - .5f / sigma * flag, (max - mean) / sigma + .5f / sigma * flag))); } validate(); } }