Poisson Distribution - Lab

Introduction

In this lab, you will put your knowledge of the Poisson Distribution to use to solve some sample real-world problems!

Objectives

You will be able to:

• Calculate the probabilities of certain events that follow a Poisson distribution

Instructions

Solve the following sample problems by using Python and your knowledge of the Poisson Distribution.

Getting Started

Good Data Scientists plan ahead! Since you're going to be solving Poisson Distribution problems in this lab, it's probably a good idea to write a function that calculates Poisson Probabilities for us first.

Recall that the Poisson Probability Formula is:

$$p(x) = \frac{\lambda^xe^{-\lambda}}{x!}$$

Write a generalized function that takes in the appropriate parameters and returns the Poisson Probability.

NOTE: You can use np.exp() to quickly calculate $e$, and math.factorial (from the math library, not numpy) to calculate factorials.

HINT: It's up to you whether or not you have your function calculate the value for lambda given $\mu$ and the interval, or whether you calculate lambda yourself beforehand and just pass it into the function.

import numpy as np
from math import factorial

def poisson_probability(lambd, x):
    pass

Question 1

A fireman fights, on average, 4 fires per month. What is the probability that a fireman is called to two different fires this week?

lambd_q1 = None
prob_q1 = None
print(prob_q1)  # Expected Output:  0.18393972058572117

Question 2

A car salesman sells an average of 4 cars per week. What is the probability they sell a car today?

lambd_q2 = None
prob_q2 = None
print(prob_q2)  # Expected Output: 0.32269606971871956

Question 3

A website makes an average of 50 sales per day. What is the probability that they make 3 sales in an hour?

lambd_q3 = None
prob_q3 = None
print(prob_q3)  # Expected Output: 0.18764840049328912

Question 4

A factory produces 250 cars per week (assume that the factory runs day and night all week with no down time). What is the probability that they produce 3 cars in the next hour?

lambd_q4 = None
prob_q4 = None
print(prob_q4)   # Expected Output: 0.1240136186052091

Question 5

The following table shows the number of houses sold by a realtor each week for the month of May. What is the probability that they sell 3 houses next week?

mean_weekly_sales = None
lambd_q5 = None 
prob_q5 = None
print(prob_q5)  # Expected Output: 0.18250047186175347

Summary

In this lab, we got some practice making use of our knowledge of the Poisson Distribution to answer some real-world questions!