Introduction to Probability – The Science of Uncertainty

An introduction to probabilistic models, including random processes and the basic elements of statistical inference.

About The Course

*Note - This is an Archived course*

This is a past/archived course. At this time, you can only explore this course in a self-paced fashion. Certain features of this course may not be active, but many people enjoy watching the videos and working with the materials. Make sure to check for reruns of this course. 

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 essentially the same as those of the corresponding MIT class (Probabilistic Systems Analysis and Applied Probability) -- a course that has been offered and continuously refined over more than 50 years. It is a challenging class, but it will enable you to apply the tools of probability theory to real-world applications or your research.

Recommended Background

College-level calculus (single-variable and multivariable). Although this is not a mathematics course, it does rely on the language and some tools from mathematics. It requires a level of comfort... see more...