Poisson Distribution

import numpy as np
import matplotlib.pyplot as plt
import scipy as sp

Examples on webpage

# 1
X = sp.stats.poisson(3.5)

# 1a
X.pmf(2)

0.18495897346170082

# 1b
1 - np.sum(X.pmf(np.arange(3)))

0.6791528011378659

np.sum(X.pmf(np.arange(3, 1000)))

0.679152801137866

# made up question
# what's the probability of an even number of earthquakes
np.sum(X.pmf(np.arange(1000) * 2))

0.5004559409827773

x = np.arange(1000)
ind = x % 2 == 0
np.sum(X.pmf(x[ind]))

0.5004559409827773

# 1c
Y = sp.stats.poisson(3.5 * 7)
np.sum(Y.pmf(np.arange(6)))

2.091682196839196e-06

3.5 * 7

24.5

# 2
X = sp.stats.poisson(5)

# 2a
X.pmf(7)

0.10444486295705395

# 2b
np.sum(X.pmf(np.arange(4)))

0.26502591529736164

# 2c
Y = sp.stats.poisson(5 * 2)

1 - np.sum(Y.pmf(np.arange(11)))

0.4169602498070133