w2l408_flip3.py

import random, pylab

#set line width
pylab.rcParams['lines.linewidth'] = 6
#set font size for titles 
pylab.rcParams['axes.titlesize'] = 20
#set font size for labels on axes
pylab.rcParams['axes.labelsize'] = 20
#set size of numbers on x-axis
pylab.rcParams['xtick.major.size'] = 5
#set size of numbers on y-axis
pylab.rcParams['ytick.major.size'] = 5



def stdDev(X):
    mean = sum(X)/float(len(X))
    tot = 0.0
    for x in X:
        tot += (x - mean)**2
    return (tot/len(X))**0.5






##vals = []
##for i in range(100000):
##    num = random.random()
##    vals.append(num)
##pylab.hist(vals, bins = 11)
##xmin, xmax = pylab.xlim()
##ymin, ymax = pylab.ylim()
##print 'x-range =', xmin, '-', xmax
##print 'y-range =', ymin, '-', ymax
##pylab.figure
##pylab.hist(vals, bins = 11)
###pylab.xlim(-1.0, 2.0)
##pylab.show()
##assert False















def flip(numFlips):
    heads = 0.0
    for i in range(numFlips):
        if random.random() < 0.5:
            heads += 1.0
    return heads/numFlips

def flipSim(numFlipsPerTrial, numTrials):
    fracHeads = []
    for i in range(numTrials):
        fracHeads.append(flip(numFlipsPerTrial))
    mean = sum(fracHeads)/len(fracHeads)
    sd = stdDev(fracHeads)
    return (fracHeads, mean, sd)

def labelPlot(numFlips, numTrials, mean, sd):
    pylab.title(str(numTrials) + ' trials of '
                + str(numFlips) + ' flips each')
    pylab.xlabel('Fraction of Heads')
    pylab.ylabel('Number of Trials')
    xmin, xmax = pylab.xlim()
    ymin, ymax = pylab.ylim()
    pylab.text(xmin + (xmax-xmin)*0.02, (ymax-ymin)/2,
               'Mean = ' + str(round(mean, 4))
               + '\nSD = ' + str(round(sd, 4)))

def makePlots(numFlips1, numFlips2, numTrials):
    val1, mean1, sd1 = flipSim(numFlips1, numTrials)
    pylab.hist(val1, bins = 21)
    xmin,xmax = pylab.xlim()
    ymin,ymax = pylab.ylim()
    labelPlot(numFlips1, numTrials, mean1, sd1)
    pylab.figure()
    val2, mean2, sd2 = flipSim(numFlips2, numTrials)
    pylab.hist(val2, bins = 21)
    pylab.xlim(xmin, xmax)
    ymin, ymax = pylab.ylim()
    labelPlot(numFlips2, numTrials, mean2, sd2)

pylab.seed(0)    
makePlots(100,1000,100000)
pylab.show()