# Probability - The Science of Uncertainty and Data

Provided by Massachusetts Institute of Technology (MITx)
Free

\$300 USD for graded exams and assignments, plus a certificate

Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference — Course 1 of 4 in the MITx MicroMasters program in Statistics and Data Science.

Start Date:Apr 25, 2019

### Before you start

College-level calculus (single-variable & multivariable). Comfort with mathematical reasoning; and familiarity with sequences, limits, infinite series, the chain rule, and ordinary or multiple integrals.

#### Learning on edX

In this instructor-paced course, plan to complete the course within the defined time period.

## What you will learn

• The basic structure and elements of probabilistic models
• Random variables, their distributions, means, and variances
• Probabilistic calculations
• Inference methods
• Laws of large numbers and their applications
• Random processes

## Overview

The world is full of uncertainty: accidents, storms, unruly financial markets, noisy communications. The world is also full of data. Probabilistic modeling and the related field of statistical inference are the keys to analyzing data and making scientifically sound predictions.

Probabilistic models use the language of mathematics. But instead of relying on the traditional "theorem-proof" format, we develop the material in an intuitive -- but still rigorous and mathematically-precise -- manner. Furthermore, while the applications are multiple and evident, we emphasize the basic concepts and methodologies that are universally applicable.

The course covers all of the basic probability concepts, including:
• multiple discrete or continuous random variables, expectations, and conditional distributions
• laws of large numbers
• the main tools of Bayesian inference methods
• an introduction to random processes (Poisson processes and Markov chains)
The contents of this course are heavily based upon the corresponding MIT class --  Introduction to Probability -- a course that has been offered and continuously refined over more than 50 years.  It is a challenging class but will enable you to apply the tools of probability theory to real-world applications or to your research.

This course is part of the MITx MicroMasters Program in Statistics and Data Science. Master the skills needed to be an informed and effective practitioner of data science. You will complete this course and three others from MITx, at a similar pace and level of rigor as an on-campus course at MIT, and then take a virtually-proctored exam to earn your MicroMasters, an academic credential that will demonstrate your proficiency in data science or accelerate your path towards an MIT PhD or a Master's at other universities. To learn more about this program, please visit https://micromasters.mit.edu/ds/.

## Learner testimonials

“This is by far the best probability & statistics course available--online or in the classroom.”

"You won’t find another intro to probability with greater depth and breadth."

"This is a great course for those serious about forming a solid foundation in probability."

"[This course] has created a love for probabilistic models, that, I guess, truly govern everything around us."

"This should be in top 10 MOOCs of all time."

How is this class related to 6.041x?
The material covered, and the resources (videos, etc.) are largely the same, but homeworks and exams contain revised and new problems.

What textbook do I need for the course?
None - there is no required textbook. The class follows closely the text Introduction to Probability, 2nd edition, by Bertsekas and Tsitsiklis, Athena Scientific, 2008. (See the publisher's website or Amazon.com for more information.) However, while this textbook is recommended as supplemental reading, the materials provided by this course are self-contained.

What is the format of the class?
The course material is organized along units, each unit containing between one and three lecture sequences. (For those who purchase the textbook, each unit corresponds to a chapter.) Each lecture sequence consists of short video clips, interwoven with short problems to test your understanding. Each unit also contains a wealth of supplementary material, including videos that go through the solutions to various problems.

How much do I need to work for this class?
This is an ambitious class in that it covers a lot of material in substantial depth. In addition, MIT considers that the best way to master the subject is by actually solving on your own a fair number of problems. MIT students who take the corresponding residential class typically report an average of 11-12 hours spent each week, including lectures, recitations, readings, homework, and exams.