#Roll of two dice.

#Compute probabilites for the roll of two dice.
#The value returned is an array of the cardinality
#of the frequencies of the events X=i for i from
#2 through 12.

from pylab import *

def dice_frequencies():
    #generate the sample space
    s=[(i,j) for i in range(1,7) for j in range(1,7)]
    t=[sum(pair) for pair in s]
    h=histogram(t,bins=arange(1.5,13,1))
    return h[0]

#Use the cumulative distribution function to simulate 100,000
#samples from this distribution.  Then obtain a histogram of the
#relative frequencies and plot them side by side with the
#theoretically derived probabilities.

def display():
    y=dice_frequencies()/36
    z=cumsum(y)
    stem(arange(2,13),y,label='computed',linefmt='r-',markerfmt='k.')
    samples=[2+searchsorted(z,random()) for j in range(100000)]
    h=histogram(samples,bins=arange(1.5,13,1))
    stem(arange(2.2,13.2,1),h[0]/100000,label='simulated',linefmt='k-',markerfmt='r.')
    
    title('PMF of sum of two dice')
    legend(loc='upper right')
    show()