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Fundamentals of Probability, Fall 2008

(Complete Item 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 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.

Subject:: Mathematics and Statistics
Grade Level:: Post-secondary
Collection:: MIT OpenCourseWare

Probabilistic Systems Analysis and Applied Probability, Fall 2010

(Complete Item Description)

Abstract:: Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference. Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example: The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of "The Ten Things Everyone Should Know About Science". A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions. Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget. The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Subject:: Mathematics and Statistics, Science and Technology, Social Sciences
Grade Level:: Post-secondary
Collection:: MIT OpenCourseWare

Probability: Poisson Process (1of 2)

(Complete Item Description)

Abstract:: This is an introduction to Poisson Processes and the Poisson Distribution. [Probability playlist: Lesson 27 of 29]

Subject:: Mathematics and Statistics
Grade Level:: Secondary
Collection:: Khan Academy

Probability: Poisson Process (2 of 2)

(Complete Item Description)

Abstract:: This lesson explains more of the drivation of the Poisson Distribution. [Probability playlist: Lesson 28 of 29]

Subject:: Mathematics and Statistics
Grade Level:: Secondary
Collection:: Khan Academy

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