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6.436J Fundamentals of Probability (MIT) 6.436J Fundamentals of Probability (MIT)

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 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations. 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 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.Subjects

sample space | sample space | random variables | random variables | expectations | expectations | transforms | transforms | Bernoulli process | Bernoulli process | Poisson process | Poisson process | Markov chains | Markov chains | limit theorems | limit theorems | measure theory | measure theoryLicense

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See all metadata18.125 Measure and Integration (MIT) 18.125 Measure and Integration (MIT)

Description

This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform. This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.Subjects

Lebesgue integral | Lebesgue integral | convergence theorems | convergence theorems | Lebesgue measure in Rn | Lebesgue measure in Rn | Lpspaces | Lpspaces | Radon-Nikodym Theorem | Radon-Nikodym Theorem | Lebesgue Differentiation Theorem | Lebesgue Differentiation Theorem | Fubini Theorem | Fubini Theorem | Hausdorff measure | Hausdorff measure | Area and Coarea Formulas | Area and Coarea Formulas | measure theory | measure theory | convolution | convolution | Fourier transform | Fourier transform | Lebesque Integration Theory | Lebesque Integration TheoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata18.125 Measure and Integration (MIT)

Description

This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.Subjects

Lebesgue integral | convergence theorems | Lebesgue measure in Rn | Lpspaces | Radon-Nikodym Theorem | Lebesgue Differentiation Theorem | Fubini Theorem | Hausdorff measure | Area and Coarea Formulas | measure theory | convolution | Fourier transform | Lebesque Integration TheoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata6.436J Fundamentals of Probability (MIT)

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 (sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, limit theorems) but at a faster pace and in more depth. There are also a number of additional topics, such as language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; deeper understanding of conditional distributions and expectations.Subjects

sample space | random variables | expectations | transforms | Bernoulli process | Poisson process | Markov chains | limit theorems | measure theoryLicense

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htmSite sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata