Poisson distribution

'''
Poisson distribution is used to describe the number of times a certain event occurs within a fixed time or space interval.
The Poisson distribution is defined by the rate parameter, symbolized by the Greek letter lambda, λ.
Lambda represents the expected value — or the average value — of the distribution.
'''
import scipy.stats as stats

# average number of calls in our call center between 9am and 10am to be 15 calls - second parameter
# What is the probability that we would see exactly 15 calls in that time frame? - first parameter
# second parameter: Poisson distributed” with lambda = 15 (average)
prob_15 = stats.poisson.pmf(15, 15)

print(prob_15)

# probability we would get between 7 and 9 calls?
prob_7_to_9 = stats.poisson.pmf(7, 15) + stats.poisson.pmf(8, 15) + stats.poisson.pmf(9, 15)

print(prob_7_to_9)

# for a range of values use cdf

# probability of observing more than 20 calls - use 1 minus
prob_more_than_20 = 1 - stats.poisson.cdf(20, 15)

print(prob_more_than_20)

# probability of observing between 17 to 21 calls
prob_17_to_21 = stats.poisson.cdf(21, 15) - stats.poisson.cdf(16, 15)

print(prob_17_to_21)