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

Poisson = st.poisson

X = Poisson(3.5)
X.pmf(2)

0.18495897346170082

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

0.6791528011378659

np.sum(X.pmf(np.arange(3, 10000)))

0.679152801137866

# 2
X = Poisson(5)
X.pmf(7)

0.10444486295705395

np.sum(X.pmf(np.arange(4)))

0.26502591529736164

Y = Poisson(10)
1 - np.sum(Y.pmf(np.arange(11)))

0.4169602498070133

X = Poisson(5)
X.pmf(3) # a
X.pmf(0) # b
Y = Poisson(20) # c
1 - np.sum(Y.pmf(np.arange(21)))

0.44090741576867676