Create Central_Limit_Theorem_Visualization_in_the_Bizarrely_Universe.java

Author: sksalahuddin2828

Central_Limit_Theorem_Visualization_in_the_Bizarrely_Universe.java

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+import java.util.Random;
+import org.apache.commons.math3.stat.descriptive.moment.Mean;
+import org.apache.commons.math3.distribution.NormalDistribution;
+
+public class CentralLimitTheoremAnimation {
+    public static double[][] generateBizarrelyUniverse(int numGalaxies, int numDimensions) {
+        Random random = new Random();
+        double[][] galaxies = new double[numGalaxies][numDimensions];
+        for (int i = 0; i < numGalaxies; i++) {
+            for (int j = 0; j < numDimensions; j++) {
+                galaxies[i][j] = random.nextGaussian();
+            }
+        }
+        return galaxies;
+    }
+
+    public static double[] centralLimitTheorem(int numGalaxies, int numDimensions, int numSamples, int sampleSize) {
+        double[] sampleMeans = new double[numSamples];
+        for (int s = 0; s < numSamples; s++) {
+            double[][] galaxies = generateBizarrelyUniverse(numGalaxies, numDimensions);
+            double[] sample = new double[sampleSize];
+            for (int i = 0; i < sampleSize; i++) {
+                sample[i] = galaxies[i][0]; // Take the first dimension for simplicity
+            }
+            Mean mean = new Mean();
+            sampleMeans[s] = mean.evaluate(sample);
+        }
+        return sampleMeans;
+    }
+
+    public static void main(String[] args) {
+        int numGalaxies = 1000;
+        int numDimensions = 3;
+        int numSamples = 100;
+        int sampleSize = 10;
+
+        // Step 5: Explanation
+        System.out.println("Welcome to the CLT Bizarrely Universe!");
+        System.out.println("In this universe, galaxies are randomly scattered in a 3D space.");
+        System.out.println("Let's visualize the Bizarrely Universe:");
+
+        double[][] galaxies = generateBizarrelyUniverse(numGalaxies, numDimensions);
+
+        // Visualization of the Bizarrely Universe
+        // Your Java plotting code goes here
+
+        System.out.println("\nNow, let's apply the Central Limit Theorem.");
+        System.out.println("We'll take " + numSamples + " samples of size " + sampleSize +
+                " and observe how their means converge to a Gaussian distribution.");
+        System.out.println("Creating the animation...");
+
+        double[] sampleMeans = centralLimitTheorem(numGalaxies, numDimensions, numSamples, sampleSize);
+
+        // Animation of the Central Limit Theorem
+        // Your Java plotting code goes here
+    }
+}