import numpy as np
import scipy.stats as st
import matplotlib.pyplot as plt

Poisson examples from https://roualdes.us/lecturenotes/poisson

# 1. 
P = st.poisson(3.5) # random variable with rate parameter

# a.
P.pmf(2) # density function, probability mass function

0.18495897346170082

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

0.6791528011378659

# c.
P = st.poisson(3.5 * 7) # average per week
np.sum(P.pmf(np.arange(6)))

2.091682196839196e-06