interesting quiz.py

''' In what follows all number are uniformly distributed on [0,1]. Start with
 a number So and the keep on generating the sequence S1,S2....until, for some
  N, Sn > So for the first time. What is the expected value E(N) of that N ? '''

import statistics
import random

# we proceed with Montecarlo method

Series_of_n = []  #we creat a list of 10 million elements (n = 10.000.000)
for i in range (10000000):
    So = float(random.uniform(0,1)) # So of the ith trial
    n = 1    # the first attempt after generating the initial number So
    while True:
        Sn = float(random.uniform(0,1))
        if Sn > So:        #for every 10 million trial, we block the while cicle we at the first Sn > So
            Series_of_n.append(n)
            break
        else:
            n += 1      #if Sn < So, the while cicle continues and n = n + 1



print(statistics.mean(Series_of_n)) #the mean of the elements in the list