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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 sample space, random variables, expectations, transforms, Bernoulli and Poisson processes, finite Markov chains, and limit theorems. There is also a number of additional topics such as: language, terminology, and key results from measure theory; interchange of limits and expectations; multivariate Gaussian distributions; and deeper understanding of conditional distributions and expectations.
- Subject:
- Mathematics
- Statistics and Probability
- Material Type:
- Full Course
- Provider:
- MIT
- Provider Set:
- MIT OpenCourseWare
- Author:
- Polyanskiy, Yury
- Date Added:
- 09/01/2018