central limit theorem demonstration

clt.py

#!/usr/bin/python

import math
import random

def bernoulli(p=0.5):
    """Bernoulli random variable with parameter p."""
    return 1 if random.random() < p else 0

def bernoulli_sum(n, p=0.5):
    """Sum of n Bernoulli random variables (ranges between 0 and n)."""
    return sum((bernoulli(p) for _ in xrange(n)))

def bernoulli_avg(n, p=0.5):
    """Average of n Bernoulli random variables (ranges between 0 and 1)."""
    return bernoulli_sum(n, p) / float(n)

if __name__ == '__main__':
    num_trials = 10
    n = 100000
    p = .5
    sum_mean = n * p
    sum_approx_stdev = math.sqrt(n * p * (1-p))
    avg_mean = p
    avg_approx_stdev = math.sqrt(p * (1-p) / n)

    print "Sums of %d Bernoulli random variables with parameter %f, mean = %f, stdev approx %f" % (n, p, sum_mean, sum_approx_stdev)
    for _ in xrange(num_trials):
        print bernoulli_sum(n, p)

    print "Averages of %d Bernoulli random variables with parameter %f, mean = %f, stdev approx %f" % (n, p, avg_mean, avg_approx_stdev)
    for _ in xrange(num_trials):
        print bernoulli_avg(n, p)