Most popular programs
Trending now
Build foundational knowledge of data science with this introduction to probabilistic models, including random processes and the basic elements of statistical inference -- Part of the MITx MicroMasters program in Statistics and Data Science.
332,660 already enrolled!
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:
The contents of this courseare 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 theMITx 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/.
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.
Unit 1: Probability models and axioms
Unit 2: Conditioning and independence
Unit 3: Counting
Unit 4: Discrete random variables
Unit 5: Continuous random variables
Unit 6: Further topics on random variables
Unit 7: Bayesian inference
Unit 8: Limit theorems and classical statistics
Unit 9: Bernoulli and Poisson processes
Unit 10 (Optional): Markov chains
“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 I ntroduction 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,interwovenwith 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.
Who can take this course?
Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.
Who can take this course?
Unfortunately, learners residing in one or more of the following countries or regions will not be able to register for this course: Iran, Cuba and the Crimea region of Ukraine. While edX has sought licenses from the U.S. Office of Foreign Assets Control (OFAC) to offer our courses to learners in these countries and regions, the licenses we have received are not broad enough to allow us to offer this course in all locations. edX truly regrets that U.S. sanctions prevent us from offering all of our courses to everyone, no matter where they live.
