import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import poisson

mu = 4.5
E = 0.
x = np.linspace(0.,15.,16)
y = poisson.pmf(x,mu)
for n,p in zip(x,y):
    E += p*n
print("Expectation:", E)

fig = plt.figure(figsize=(6,6), dpi=80)
plt.bar(x,y)
plt.show()