6.436J / 15.085J Fundamentals of Probability, Fall 2005
Name
6-436j-fall-2005/contents/index.htm
Size
15.78 KB
Format
HTML
Checksum (MD5)
a462cc636225124496e818e610ed1bc8
Author(s)
Tsitsiklis, John
Alternative Title
Fundamentals of Probability
Date Issued
December 2005
Abstract
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.
Subjects
Introduction to probability theory
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 process
Finite-state Markov chains
Convergence notions and their relations
Limit theorems
Familiarity with elementary notions in probability and real analysis is desirable
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
Massachusetts Institute of Technology. Department of Economics
Massachusetts Institute of Technology. Engineering Systems Division
Massachusetts Institute of Technology. Department of Materials Science and Engineering
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
Sloan School of Management
Massachusetts Institute of Technology. Department of Urban Studies and Planning
Terms of Use
Persistent DSpace Link
