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  1. // Problem 3: Normal Distribution (Box-Muller)
  2.  
  3. #include <bits/stdc++.h>
  4. using namespace std;
  5.  
  6. int main() {
  7.     srand(time(0));
  8.     int N = 20000;   
  9.     double sum = 0, sumSq = 0;
  10.     int pairs = N / 2;   
  11.  
  12.     cout << "Generating " << N << " normal random values...\n";
  13.  
  14.     for (int i = 0; i < pairs; i++) {
  15.         double u1 = (rand() + 1.0) / (RAND_MAX + 1.0);
  16.         double u2 = (rand() + 1.0) / (RAND_MAX + 1.0);
  17.  
  18.         double z0 = sqrt(-2.0 * log(u1)) * cos(2 * M_PI * u2);
  19.         double z1 = sqrt(-2.0 * log(u1)) * sin(2 * M_PI * u2);
  20.  
  21.         sum += z0 + z1;
  22.         sumSq += z0 * z0 + z1 * z1;
  23.     }
  24.  
  25.     double mean = sum / N;
  26.     double variance = (sumSq / N) - mean * mean;
  27.     double stddev = sqrt(variance);
  28.  
  29.     cout << "\nStatistics:\n";
  30.     cout << "Mean       : " << mean << endl;
  31.     cout << "StdDev     : " << stddev << endl;
  32.  
  33.     return 0;
  34. }
  35.  
  36. /*
  37. Q1. Does your distribution resemble a bell curve?
  38. = Yes. The generated numbers follow a bell-shaped (Normal) distribution.
  39.  
  40. Q2. What is the mean and stddev? Are they close to 0 and 1?
  41. = Mean is approximately 0 and StdDev approximately 1. Randomness causes slight variations, 
  42.   but repeated runs confirm they stay near 0 and 1.
  43. */
  44.  
Success #stdin #stdout 0.01s 5316KB
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Standard input is empty
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Generating 20000 normal random values...

Statistics:
Mean       : 0.00203272
StdDev     : 1.00312
https://ideone.com/PgcCDt
language:
C++ (gcc 8.3)
created:
6 days ago
visibility:
public

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