Test the Law Of Large Numbers

for N random normally distributed numbers 

with mean = 0, stdev = 1:

Create a Python script that will count how many of these numbers fall between -1
and 1 and divide by the total quantity of N

You know that E(X) = 68.2%

Check that Mean(XN) -> E(X) as you rerun your script while increasing N
In [5]:
from IPython.display import Image
from IPython.core.display import HTML 
Image(url= "normaldistribution.jpg", width=600)
Out[5]:
In [8]:
import numpy as np
from numpy.random import randn

n = 100000
counter = 0

for i in randn(n):
    if -1 < i and i < 1:
        counter +=1
    result = counter/n
    
print(result)        

0.68246

Result:

- by increasing the n, we are getting closer & closer to 68.2%