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6.436J / 15.085J Fundamentals of Probability, Fall 2005

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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


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