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Last updated:

December 1, 2022


Unlimited Duration


This course includes:

Unlimited Duration

Badge on Completion

Certificate of completion

Unlimited Duration


Welcome to 6.041/6.431, a subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference.

Nowadays, there is broad consensus that the ability to think probabilistically is a fundamental component of scientific literacy. For example:

  • The concept of statistical significance (to be touched upon at the end of this course) is considered by the Financial Times as one of “The Ten Things Everyone Should Know About Science”.
  • A recent Scientific American article argues that statistical literacy is crucial in making health-related decisions.
  • Finally, an article in the New York Times identifies statistical data analysis as an upcoming profession, valuable everywhere, from Google and Netflix to the Office of Management and Budget.

The aim of this class is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition.

Course Curriculum

  • Probability Models and Axioms Unlimited
  • Conditioning and Bayes’ Rule Unlimited
  • Independence Unlimited
  • Counting Unlimited
  • Discrete Random Variables; Probability Mass Functions; Expectations Unlimited
  • Discrete Random Variable Examples; Joint PMFs Unlimited
  • Multiple Discrete Random Variables: Expectations, Conditioning, Independence Unlimited
  • Continuous Random Variables Unlimited
  • Multiple Continuous Random Variables Unlimited
  • Continuous Bayes’ Rule; Derived Distributions Unlimited
  • Derived Distributions; Convolution; Covariance and Correlation Unlimited
  • Iterated Expectations; Sum of a Random Number of Random Variables Unlimited
  • Bernoulli Process Unlimited
  • Poisson Process – I Unlimited
  • Poisson Process – II Unlimited
  • Markov Chains – I Unlimited
  • Markov Chains – II Unlimited
  • Markov Chains – III Unlimited
  • Weak Law of Large Numbers Unlimited
  • Central Limit Theorem Unlimited
  • Bayesian Statistical Inference – I Unlimited
  • Bayesian Statistical Inference – II Unlimited
  • Classical Statistical Inference – I Unlimited
  • Classical Inference – II Unlimited
  • Classical Inference – III; Course Overview Unlimited

About the instructor

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Massachusetts Institute of Technology