Created
October 5, 2019 09:16
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import math | |
import matplotlib.pyplot as plt | |
import numpy as np | |
import random | |
import scipy.stats as stats | |
die_e = 3.5 # expected value of an ordinary six-sided die | |
die_var = 17.5/6 # variance of an ordinary six-sided die | |
die_sigma = math.sqrt(die_var) | |
def create_statistics(): | |
clt_sum_frequencies = np.zeros(601, dtype = int) | |
lln_averages = [] | |
total_sum = 0 | |
for repetition in range(0, 10000): | |
sum = 0 | |
for cast in range(0, 100): | |
die_number = random.randint(1, 6) | |
sum = sum + die_number | |
clt_sum_frequencies[sum] += 1 | |
total_sum += sum | |
lln_averages.append(total_sum / (100 * (repetition + 1))) | |
return clt_sum_frequencies / 10000, lln_averages | |
def plot_clt_chart(sum_frequencies, shift, scale): | |
sums = np.linspace( | |
(0 - shift) / scale, | |
(600 - shift) / scale, | |
len(sum_frequencies)) | |
width = sums[1] - sums[0] | |
sum_densities = sum_frequencies / width | |
mu = 100 * die_e - shift | |
sigma = die_sigma * math.sqrt(100) / scale | |
normal_densities = [stats.norm.pdf(x, mu, sigma) for x in sums] | |
min_x = 280 | |
max_x = 420 | |
plot_chart( | |
sums[min_x:max_x], | |
sum_densities[min_x:max_x], | |
normal_densities[min_x:max_x], | |
width) | |
def plot_lln_chart(averages): | |
mu = die_e | |
indexes = np.arange(len(averages)) | |
plt.ylim(3.48, 3.52) | |
plot_chart(indexes, averages, [mu for x in indexes]) | |
def plot_chart(x_values, y_values, y_comparison_values, width=1.0): | |
plt.bar(x_values, y_values, width=width, align='center') | |
plt.plot(x_values, y_comparison_values, color='r') | |
plt.show() | |
clt_sum_frequencies, lln_averages = create_statistics() | |
plot_clt_chart(clt_sum_frequencies, 0, 1) | |
plot_lln_chart(lln_averages) |
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