FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

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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Massachusetts Institute of Technology

November 3, 2022

UK

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Last updated:

November 3, 2022

Duration:

Unlimited Duration

FREE

This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration

Description

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

Course Curriculum

  • 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

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Massachusetts Institute of Technology