In this lesson, we'll make use of newfound knowledge of the Exponential Distribution to answer some real-world questions!
You will be able to:
- Understand and explain the Exponential Distribution and its use cases.
Before we can begin answering questions, it will probably be helpful to write some python functions to quickly calculate the PDF and CDF for us.
For reference, here are the functions we'll want to implement.
In the cell below, complete the following functions.
import numpy as np
def exp_pdf(mu, x):
pass
def exp_cdf(mu, x):
pass
Great! Now, lets answer some questions.
Steven is picking up a friend at the airport, and their plane is late. The late flight is 22 minutes behind schedule. What is the probability that Steven will wait 30 minutes or less for his friend's flight to land?
# Expected Output: 0.7442708400868994
The average student takes 44 minutes to complete a test. What is the probability that the fastest student in the class will take 38 minutes to complete the test?
# Expected Output: 0.00958241148834099
The first customer of the day walks into a store 6 minutes after the store opens, on average. What is the probability that a customer shows up within 8 minutes of opening tomorrow?
# Expected Output: 0.7364028618842733
The average interval that calls come in at a call center is 8 seconds. What is the probability that the nexts call will happen in 7 seconds?
# Expected Output: 0.05210775245981355
The average earthquake in a given region happens every 7 weeks. What is probability that the next earthquake happens between 5 and 8 weeks from now?
Hint: This has both an upper and lower bound. You'll need to do some arithmetic to solve this one.
lower_bound = None
upper_bound = None
print("Probability of earthquake before 5 weeks: {}%".format(lower_bound * 100))
print("Probability of earthquake before 8 weeks: {}%".format(upper_bound * 100))
print("Probability of earthquake between 5 - 8 weeks: {}%".format((upper_bound - lower_bound) * 100))
# Expected Output:
#
# Probability of earthquake before 5 weeks: 51.045834044304684%
# Probability of earthquake before 8 weeks: 68.10934426760295%
# Probability of earthquake between 5 - 8 weeks: 17.063510223298273%
In this lesson, we solved some real-world problems using the PDF and CDF for the Exponential Distribution!