6.436J / 15.085J Fundamentals of Probability

Fall 2005

Probability of finding a red card in black cards.
Probability can be used to determine the likelihood of finding a red card in a stack of black cards. (Image courtesy of stock.xchng.)

Course Highlights

This course features exams given in the course and a list of topics and associated readings in the readings section. Lecture notes are still under development.

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 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.
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Prof. John Tsitsiklis

Course Meeting Times

Two sessions / week
1.5 hours / session

One session / week
1 hour / session