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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.

Assessment

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.

Certification

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Course Credit: MIT

Course Curriculum

Module 01
Probabilistic models and probability measures 00:15:00
Two fundamental probabilistic models 00:15:00
Conditioning and independence 00:10:00
Counting 00:05:00
Random variables 00:15:00
Discrete random variables and their expectations Part 1 00:20:00
Discrete random variables and their expectations Part 2 00:20:00
Continuous random variables Part 1 00:10:00
Continuous random variables Part 2 00:15:00
Derived distributions 00:15:00
Abstract integration Part 1 00:15:00
Abstract integration Part 2 00:10:00
Product measure and Fubini’s theorem 00:10:00
Module 02
Moment generating functions 00:10:00
Multivariate normal distributions 00:10:00
Multivariate normal distributions characteristic functions 00:10:00
Convergence of random variables 00:10:00
Laws of large numbers Part 1 00:05:00
Laws of large numbers Part 2 00:10:00
The Bernoulli and Poisson processes 00:10:00
The Poisson process 00:05:00
Markov Chains 00:10:00
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
Birth-death processes 00:10:00
Assessment
Submit Your Assignment 00:00:00
Certification 00:00:00

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