Monte Carlo

import math
import numpy as np
import random


def get_rand_number(min_value, max_value):
    _range = max_value - min_value
    choice = random.uniform(0,1)
    return min_value + _range*choice


def f_of_x(x):
    return x**2


def crude_monte_carlo(num_samples=5000):
    lower_bound = 0
    upper_bound = 1
    sum_of_samples = 0

    for i in range(num_samples):
        x = get_rand_number(lower_bound, upper_bound)
        sum_of_samples += f_of_x(x)

    return (upper_bound - lower_bound) * float(sum_of_samples/num_samples)






n = [10, 20, 50, 500, 1000, 10000]

for i in range (0, 6):
    fs = crude_monte_carlo(n[i])
    print(fs, '\t', abs(fs - 1./3))