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Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inferenceLicense

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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This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inferenceLicense

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 metadata6.436J 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

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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This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inferenceLicense

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 metadataSample Space and Tree Diagrams

Description

Homework, Interactive resources and resource sheets on sample space and tree diagrams (word and excel)Subjects

sample space | tree diagrams | interactive | resources | word | excel | .doc | .xls | SCIENCES and MATHEMATICS | RLicense

Attribution-Noncommercial 2.0 UK: England & Wales Attribution-Noncommercial 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc/2.0/uk/ http://creativecommons.org/licenses/by-nc/2.0/uk/Site sourced from

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See all metadata6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inferenceLicense

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 metadata6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inferenceLicense

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-allarchivedcourses.xmlAttribution

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See all metadata6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inferenceLicense

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

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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

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