This is an archived course. A more recent version may be available at

Fundamentals of Probability

As taught in: Fall 2005

Photo of playing cards.

Probability can be used to determine the likelihood of finding a red card in a stack of black cards. (Photo by incurable_hippie on Flickr.)


Prof. John Tsitsiklis

MIT Course Number:

6.436J / 15.085J



Course Description

This is a course on the fundamentals of probability geared towards first or second-year graduate students who are interested in a rigorous development of the subject. The course covers most of the topics in MIT course 6.431 but at a faster pace and in more depth. Topics covered include: probability spaces and measures; discrete and continuous random variables; conditioning and independence; multivariate normal distribution; abstract integration, expectation, and related convergence results; moment generating and characteristic functions; Bernoulli and Poisson processes; finite-state Markov chains; convergence notions and their relations; and limit theorems. Familiarity with elementary notions in probability and real analysis is desirable.