# script thwowCoin.py
''' example to produce random numbers (0/1) 
    as obtained by throwing a coin
.. author:: Guenter Quast <g.quast@kit.edu>

'''

# pyhton2 - python3 compatibility
from __future__ import division
from __future__ import absolute_import
from __future__ import print_function
from __future__ import unicode_literals
#
import numpy as np
import matplotlib.pyplot as plt

nthrow=500    # how often to throw

r=[]
Nh=0

for N in range(nthrow):
  if np.random.rand()>0.5:
    Nh+=1
  r.append(float(Nh)/(N+1.))

# plot result ...
x=np.linspace(0.,nthrow,nthrow)
plt.plot(x,r,'g.')
# ... and expectation ...
plt.plot(x,0.5*np.ones(nthrow),'r--',lw=2)
# ... and error band
plt.plot(x,0.5+0.5/np.sqrt(x),'b--',lw=2)
plt.plot(x,0.5-0.5/np.sqrt(x),'b--',lw=2)

plt.show()