# Seed random number generator
np.random.seed(42)
 
# Compute mean no-hitter time: tau
tau = np.mean(nohitter_times)
 
# Draw out of an exponential distribution with parameter tau: inter_nohitter_time
inter_nohitter_time = np.random.exponential(tau, 100000)
 
# Plot the PDF and label axes
_ = plt.hist(inter_nohitter_time,
    bins=50, normed=True, histtype='step')
_ = plt.xlabel('Games between no-hitters')
_ = plt.ylabel('PDF')
 
# Show the plot
plt.show()

# Create an ECDF from real data: x, y
x, y = ecdf(nohitter_times)
 
# Create a CDF from theoretical samples: x_theor, y_theor
x_theor, y_theor = ecdf(inter_nohitter_time)
 
# Overlay the plots
plt.plot(x_theor, y_theor)
plt.plot(x, y, marker='.', linestyle='none')
 
# Margins and axis labels
plt.margins(0.02)
plt.xlabel('Games between no-hitters')
plt.ylabel('CDF')
 
# Show the plot
plt.show()