# -*- coding: utf-8 -*-
import math
import random

random.seed(1234)

step_max_random_walk = 100
max_walkers = 100000
a = 8.0

xsum = 0
x2sum = 0
for j in range(1,max_walkers+1):
   x=0.0
   for i in range(1,step_max_random_walk+1):
       coin = random.random()
       if coin < 0.5:
           x = x-a
       else:
           x = x+a
   xsum = xsum + x
   x2sum = x2sum + (x*x)


print '<x>',xsum/max_walkers,'<x^2>',x2sum/max_walkers