Spread of the Poisson Distribution

import scipy.stats as stats
import numpy as np

# To observe that as the parameter lambda increases, the variance — or spread — of possible values increases as well.
# 5000 draws, lambda = 7
rand_vars_7 = stats.poisson.rvs(7, size = 5000)

# find variance & print minimum and maximum values
print(np.var(rand_vars_7)) # Output: 7.02419964
'''
Because this is calculated from a sample, it is possible that the variance might not equal EXACTLY lambda. However, we do expect it to be relatively close when the sample size is large, like in this example.
'''
print(min(rand_vars_7), max(rand_vars_7))  # Output: 0 19

# Compared to a larger lambda
# 5000 draws, lambda = 17
rand_vars_17 = stats.poisson.rvs(17, size = 5000) # Output: 16.85025136

print(np.var(rand_vars_17))
print(min(rand_vars_17), max(rand_vars_17))  # Output: 4 33 which shows these values are spread wider, indicating a larger variance.