# -*- coding: utf-8 -*-

# MSPA 400 Session #5 Python Module #2

# Reading assignment:

# “Think Python” 2nd Edition Chapter 6 (6.1-6.9)

# “Think Python” 3rd Edition Chapter 6 (pages 61-71)

# Module #1 objectives: 1) introduce binomial probabilities,

# 2) demonstrate the calculation of binomial probabilities, and 3) display

# binomial distributions. (Functions used in Module #1 will be required.)

import numpy

import matplotlib.pyplot

from matplotlib.pyplot import *

# The following three functions were used in Module #1.

def factorial(n):

if n == 0:

return 1

else:

recurse = factorial(n-1)

result = n*recurse

return result

def perm(n,k):

if n == 0:

return 1

if k > n:

return -1

else:

result=1

for i in range (0,n-k):

result=result*(n-i)

return result

def comb(n,k):

result=perm(n,k)

result=(float(result))/factorial(n-k)

result=int(result)

return result

# An example of code for calculating a binomial probability follows

# Section 5.11 of "Think Python" presents keyboard input.

# Keyboard input will be used for a binomial calculation.

# In the code which follows, note the type conversions from string to

# integer, integer to floating point and back.

print 'In each instance, hit enter after submitting the requested number.'

print 'Enter a positive integer for the number of repeated trials.'

n=raw_input()

n=int(n) # This converts n from a string to an integer.

print ('Enter the number of successes.')

k=raw_input()

k=int(k)

print ('Enter the probability of success.')

p=raw_input()

p=float(p) # This converts p from a string to a floating point number.

prob=(comb(n,k))*(p**k)*((1.0-p)**(n-k))

print 'Binomial probability with n= %r, k= %r, p= %r is %r\n' %(n,k,p,prob)

# The following example shows how to calculate a binomial distribution

# and print the result. First a binomial function will be defined. The

# values previously entered for the number of repeated trials, the

# number of successes and the probability of success will be used.

def binomial(n,k,p):

prob=(comb(n,k))*(p**k)*((1.0-p)**(n-k))

return prob

print 'Binomial distribution with %r trials and p= %r follows.\n' %(n,p)

distribution=[]

for i in range (0,n+1):

prob=binomial(n,i,p)

print '# of successes= %r probability= %1.4f ' %(i,prob)

distribution=distribution+[prob]

x=range(0,n+1,1) # x and y are both lists with the same number of elements.

y=distribution

# The plot is produced in layers. bar() places the red bars of width 0.4

# centered on x values. The heigth is determined by y. The plot()

# statement places the line plot on the chart. With only one show()

# statement, the figure() statement is unnecessary.

bar(x,y,width=0.4, align='center',color='r')

plot(x,y)

xlabel('Total Number of Trials')

ylabel('Probability of Success')

title('Binomial Probabilities ')

show()

# Exercise #1: Using a variation of the code and functions defined,

# check the calculations in Lial Section 8.4 Examples 2 and 3.

# Note the distributions which are produced.

# Exercise #2: Using the function "binomial" as defined in the code, write

# the code to verify the calculatons in Lial Section 8.5 Example 7.