import numpy as np
from scipy import stats
import matplotlib.pyplot as plt
import matplotlib.mlab as mlab
%pylab inline

#distribution of random process

mean=.5
stddev=np.sqrt(.5*.5/162)
samples=30
coinflips=np.random.normal(loc=mean, scale=stddev, size=samples)

plt.plot(coinflips,ones(len(coinflips)),'.',markersize=40, alpha=.4)
plt.xlim(mean-3.5*stddev,mean+3.5*stddev)
plt.yticks([])
plt.xlabel("% heads")

plt.show()

#probability distribution for random process

mean=.5
stddev=np.sqrt(.5*.5/162) #/162)
x = np.linspace(mean-4*stddev,mean+4*stddev,100)
plt.plot(x,mlab.normpdf(x,mean,stddev))
plt.xlim(mean-3.5*stddev,mean+3.5*stddev)
plt.xlabel("% heads")

plt.show()

#distribution of baseball winning percentage

mean=.5
stddev=.072
x = np.linspace(mean-4*stddev,mean+4*stddev,100)
plt.plot(x,mlab.normpdf(x,mean,stddev))
plt.xlim(mean-3.5*stddev,mean+3.5*stddev)
plt.xlabel("% wins")

plt.show()

mean=.5
stddev=np.sqrt(.5*.5/162)
x = np.linspace(mean-6*stddev,mean+6*stddev,100)
plt.plot(x,mlab.normpdf(x,mean,stddev),label="random")

mean=.5
stddev=.072
x = np.linspace(mean-4*stddev,mean+4*stddev,100)
plt.plot(x,mlab.normpdf(x,mean,stddev),label="baseball")
plt.xlim(mean-3.5*stddev,mean+3.5*stddev)
plt.yticks([])

plt.legend()
plt.show()