| dc.contributor.author | Tsitsiklis, John | en_US |
| dc.coverage.temporal | Fall 2005 | en_US |
| dc.date.issued | 2005-12 | |
| dc.identifier | 6.436J-Fall2005 | |
| dc.identifier | local: 6.436J | |
| dc.identifier | local: 15.085J | |
| dc.identifier | local: IMSCP-MD5-21394ea8329d4a72ac876e99c7730a75 | |
| dc.identifier.uri | http://hdl.handle.net/1721.1/73646 | |
| dc.description.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. | en_US |
| dc.language | en-US | en_US |
| dc.rights.uri | Usage Restrictions: This site (c) Massachusetts Institute of Technology 2012. Content within individual courses is (c) by the individual authors unless otherwise noted. The Massachusetts Institute of Technology is providing this Work (as defined below) under the terms of this Creative Commons public license ("CCPL" or "license") unless otherwise noted. The Work is protected by copyright and/or other applicable law. Any use of the work other than as authorized under this license is prohibited. By exercising any of the rights to the Work provided here, You (as defined below) accept and agree to be bound by the terms of this license. The Licensor, the Massachusetts Institute of Technology, grants You the rights contained here in consideration of Your acceptance of such terms and conditions. | en_US |
| dc.subject | Introduction to probability theory | en_US |
| dc.subject | Probability spaces and measures | en_US |
| dc.subject | Discrete and continuous random variables | en_US |
| dc.subject | Conditioning and independence | en_US |
| dc.subject | Multivariate normal distribution | en_US |
| dc.subject | Abstract integration | en_US |
| dc.subject | expectation | en_US |
| dc.subject | and related convergence results | en_US |
| dc.subject | Moment generating and characteristic functions | en_US |
| dc.subject | Bernoulli and Poisson process | en_US |
| dc.subject | Finite-state Markov chains | en_US |
| dc.subject | Convergence notions and their relations | en_US |
| dc.subject | Limit theorems | en_US |
| dc.subject | Familiarity with elementary notions in probability and real analysis is desirable | en_US |
| dc.title | 6.436J / 15.085J Fundamentals of Probability, Fall 2005 | en_US |
| dc.title.alternative | Fundamentals of Probability | en_US |
| dc.type | Learning Object | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Civil and Environmental Engineering | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Economics | |
| dc.contributor.department | Massachusetts Institute of Technology. Engineering Systems Division | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Materials Science and Engineering | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Mechanical Engineering | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering | |
| dc.contributor.department | Sloan School of Management | |
| dc.contributor.department | Massachusetts Institute of Technology. Department of Urban Studies and Planning | |
