Normal distribution of dice rolls: Python animation

 Since my wife started learning statistics, and I wanted to give her some intuitive understanding of the normal distribution, standard deviation, 95% confidence region etc, I made a small python code which generates an animation of the histogram of dice rolls.

This could help others time ;)

(Distribute under MIT license)

import random

import matplotlib.pyplot as plt

import numpy as np

from scipy.stats import norm

def main():

numTrial = 1000000

numDice = 20

sumResults = []

bin=np.arange(numDice-0.5, numDice*6+1.5, 1)

print(bin)

fig = plt.figure()

iFig = 1

for iTrial in range(numTrial):

sumDice = 0

for iDice in range(numDice):

sumDice += random.randint(1,6)

sumResults.append(sumDice)

if iTrial % 100 == 0:

ax = fig.add_subplot()

ax.set_title(str(numDice)+" dices case")

ax.set_xlabel("Sum of rolls")

ax.set_ylabel("Frequency")

n, bins, patches = plt.hist(sumResults,bins=bin)

loc,scale = norm.fit(sumResults)

plt.plot(bin,sum(n)*norm.pdf(bin,loc,scale),color="y")

txt = "STD:"+str(round(scale,4))

plt.text(5.0,0.01,txt,size=30)

p25 =norm.ppf(0.025 ,loc,scale)

p975=norm.ppf(0.975,loc,scale)

plt.axvline(x=p25, ymin=0.1, ymax=0.9,color="r")

plt.axvline(x=p975, ymin=0.1, ymax=0.9,color="r")

plt.savefig(str('{:05d}'.format(iFig))+".png")

iFig += 1

plt.pause(.001)

fig.clear()

if __name__ == "__main__":

main()