Relationship between Binomial and Poisson distributions You just heard that the Poisson distribution is a limit of the Binomial distribution for rare events.

BinomialPoisson.py

# Draw 10,000 samples out of Poisson distribution: samples_poisson
samples_poisson = np.random.poisson(10, size = 10000)

# Print the mean and standard deviation
print('Poisson:     ', np.mean(samples_poisson),
                       np.std(samples_poisson))

# Specify values of n and p to consider for Binomial: n, p
n = [20, 100, 1000]
p = [0.5, 0.1, 0.01]

# Draw 10,000 samples for each n,p pair: samples_binomial
for i in range(3):
    samples_binomial = np.random.binomial(n[i], p[i], size = 10000)

    # Print results
    print('n =', n[i], 'Binom:', np.mean(samples_binomial),
                                 np.std(samples_binomial))