Catalog

Probabilistic Systems Analysis and Applied Probability

Electrical Engineering and Computer Science MIT CC BY-NC-SA 4.0 25 lectures

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 {{% resource_link "89b91304-6cef-429c-8994-cc41689695bb" "recent Scientific American article" %}} argues that statistical literacy is crucial in making health-related decisions. * Finally, an {{% resource_link "67e564ff-b97f-4262-b2b9-c3fb0ce9b8df" "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.

Syllabus

  1. 1 Lecture 1: Probability Models and Axioms
  2. 2 Lecture 2: Conditioning and Bayes' Rule
  3. 3 Lecture 3: Independence
  4. 4 Lecture 4: Counting
  5. 5 Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations
  6. 6 Lecture 6: Discrete Random Variable Examples; Joint PMFs
  7. 7 Lecture 7: Multiple Discrete Random Variables: Expectations, Conditioning, Independence
  8. 8 Lecture 8: Continuous Random Variables
  9. 9 Lecture 9: Multiple Continuous Random Variables
  10. 10 Lecture 10: Continuous Bayes' Rule; Derived Distributions
  11. 11 Lecture 11: Derived Distributions; Convolution; Covariance and Correlation
  12. 12 Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables
  13. 13 Lecture 13: Bernoulli Process
  14. 14 Lecture 14: Poisson Process I
  15. 15 Lecture 15: Poisson Process II
  16. 16 Lecture 16: Markov Chains I
  17. 17 Lecture 17: Markov Chains II
  18. 18 Lecture 18: Markov Chains III
  19. 19 Lecture 19: Weak Law of Large Numbers
  20. 20 Lecture 20: Central Limit Theorem
  21. 21 Lecture 21: Bayesian Statistical Inference I
  22. 22 Lecture 22: Bayesian Statistical Inference II
  23. 23 Lecture 23: Classical Statistical Inference I
  24. 24 Lecture 24: Classical Inference II
  25. 25 Lecture 25: Classical Inference III; Course Overview

Course materials