#birthday plots

from pylab import *

def exact():
    vals=[1]
    prod =1
    for k in range(1,71):  #No need to go higher than 70 people
        prod *= (365-k)/365
        vals=concatenate((vals,[prod]))
    plot(arange(1,72),1-vals,label='exact')
    xlabel("Number of people.")
    


def approximate(): #compute and plot the same thing with the exponential
                    #approximation.
    vals=array([1])
    prod =1
    for k in range(1,71):  #No need to go higher than 70 people
        prod *= exp(-k/365)
        vals=concatenate((vals,[prod]))
    plot(arange(1,72),1-vals,label='1-exp(-k(k-1)/(2X365))')
    xlabel("Number of people.")

def approximate2(): #Use the lower bound 1-exp(-(k-1)**2/730)
    vals=array([exp(-(k-1)**2/730) for k in range(71)])
    plot(arange(1,72),1-vals,label='1-exp(-(k-1)^2/(2X365))')
##    vals=array([exp(-(k)**2/730) for k in range(71)])
##    plot(arange(1,72),1-vals,label='exp(-(k)^2/(2X365))')
    xlabel("Number of people.")
    

def do_both():
    exact()
    title("Probability of coincidental birhday (exact).")
    show()
    approximate()
    title("Proability of coincidental birthday (approximate).")
    show()
    exact()
    approximate()
    approximate2()
    legend(loc="upper left")
    title("Probability of coincidental birthday.")
    show()