This course offers 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 but at a faster pace and in more depth. There are also some additional topics such as language, and key results from measure theory, interchange of limits and expectations, multivariate Gaussian distributions, conditional distributions and expectations.
This course does not involve any written exams. Students need to answer 5 assignment questions to complete the course, the answers will be in the form of written work in pdf or word. Students can write the answers in their own time. Each answer needs to be 200 words (1 Page). Once the answers are submitted, the tutor will check and assess the work.
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Course Credit: MIT
|Probabilistic models and probability measures||00:20:00|
|Two fundamental probabilistic models||00:20:00|
|Conditioning and independence||00:15:00|
|Discrete random variables and their expectations||00:20:00|
|Discrete random variables and their expectations (cont.)||00:25:00|
|Continuous random variables||00:15:00|
|Continuous random variables (cont.)||00:15:00|
|Abstract integration (cont.)||00:10:00|
|Product measure and Fubini’s theorem||00:10:00|
|Moment generating functions||00:15:00|
|Multivariate normal distributions||00:15:00|
|Multivariate normal distributions characteristic functions||00:15:00|
|Convergence of random variables||00:15:00|
|Laws of large numbers||00:10:00|
|Laws of large numbers (cont.)||00:10:00|
|The Bernoulli and Poisson processes||00:20:00|
|The Poisson process||00:05:00|
|Markov chains II mean recurrence times||00:10:00|
|Markov chains III periodicity, mixing, absorption||00:10:00|
|Infinite Markov chains, continuous time Markov chains||00:10:00|
|Submit Your Assignment||00:00:00|
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