Book Image

Principles of Data Science

Book Image

Principles of Data Science

Overview of this book

Need to turn your skills at programming into effective data science skills? Principles of Data Science is created to help you join the dots between mathematics, programming, and business analysis. With this book, you’ll feel confident about asking—and answering—complex and sophisticated questions of your data to move from abstract and raw statistics to actionable ideas. With a unique approach that bridges the gap between mathematics and computer science, this books takes you through the entire data science pipeline. Beginning with cleaning and preparing data, and effective data mining strategies and techniques, you’ll move on to build a comprehensive picture of how every piece of the data science puzzle fits together. Learn the fundamentals of computational mathematics and statistics, as well as some pseudocode being used today by data scientists and analysts. You’ll get to grips with machine learning, discover the statistical models that help you take control and navigate even the densest datasets, and find out how to create powerful visualizations that communicate what your data means.
Table of Contents (20 chapters)
Principles of Data Science
Credits
About the Author
About the Reviewers
www.PacktPub.com
Preface
Index

Compound events


Sometimes, we need to deal with two or more events. These are called compound events. A compound event is any event that combines two or more simple events. When this happens, we need some special notation.

Given events A and B:

  • The probability that A and B occur is P(A ∩ B) = P(A and B)

  • The probability that either A or B occurs is P(A B) = P(A or B)

Understanding why we use set notation for these compound events is very important. Remember how we represented events in a universe using circles earlier? Let's say that our Universe is 100 people who showed up for an experiment, in which a new test for cancer is being developed:

In the preceding diagram, the red circle, A, represents 25 people who actually have cancer. Using the relative frequency approach, we can say that P(A) = number of people with cancer/number of people in study, that is, 25/100 = ¼ = .25. This means that there is a 25% chance that someone has cancer.

Let's introduce a second event, called B, as shown, which...