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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
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English
English [CC]
FREE
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Description
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
Course content
- Probabilistic Models and Probability Measures Unlimited
- Two Fundamental Probabalistic Models Unlimited
- Conditioning and Independence Unlimited
- Random Variables Unlimited
- Discrete Random Variables and Their Expectations Unlimited
- More on Discrete Random Variables and Their Expectations Unlimited
- Abstract Integration I Unlimited
- Abstract Integration II Unlimited
- Product Measure and Fubini’s Theorem Unlimited
- Continous Random Variables I Unlimited
- Continous Random Variables II Unlimited
- Derived Distributions Unlimited
- Moment Generating Functions Unlimited
- Multivariate Normal Distributions Unlimited
- Multivariate Normal Distributions. Characteristic Functions Unlimited
- Convergence of Random Variables Unlimited
- Laws of Large Numbers I Unlimited
- Laws of Large Numbers II Unlimited
- Uniform Integrability. Convergence of Series Unlimited
- The Basics of Stochastic Processes Unlimited
- Markov Chains I Unlimited
- Markov Chains II Unlimited
- Markov Chains III Unlimited
- Infinite Markov Chains. Continuous Time Markov Chains Unlimited
- Martingales I Unlimited
- Martingales II Unlimited
Instructor
Massachusetts Institute of Technology
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