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Course6.041 / 6.43125 lectures21 h 8 min

Probabilistic Systems Analysis and Applied Probability

Prof. John Tsitsiklis · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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.

Lectures

Video Lectures

  1. Lecture 1: Probability Models and Axioms 52 min · Video
  2. Lecture 2: Conditioning and Bayes' Rule 52 min · Video
  3. Lecture 3: Independence 47 min · Video
  4. Lecture 4: Counting 52 min · Video
  5. Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations 51 min · Video
  6. Lecture 6: Discrete Random Variable Examples; Joint PMFs 51 min · Video
  7. Lecture 7: Multiple Discrete Random Variables: Expectations, Conditioning, Independence 51 min · Video
  8. Lecture 8: Continuous Random Variables 51 min · Video
  9. Lecture 9: Multiple Continuous Random Variables 51 min · Video
  10. Lecture 10: Continuous Bayes' Rule; Derived Distributions 49 min · Video
  11. Lecture 11: Derived Distributions; Convolution; Covariance and Correlation 52 min · Video
  12. Lecture 12: Iterated Expectations; Sum of a Random Number of Random Variables 48 min · Video
  13. Lecture 13: Bernoulli Process 51 min · Video
  14. Lecture 14: Poisson Process I 53 min · Video
  15. Lecture 15: Poisson Process II 50 min · Video
  16. Lecture 16: Markov Chains I 53 min · Video
  17. Lecture 17: Markov Chains II 52 min · Video
  18. Lecture 18: Markov Chains III 52 min · Video
  19. Lecture 19: Weak Law of Large Numbers 51 min · Video
  20. Lecture 20: Central Limit Theorem 52 min · Video
  21. Lecture 21: Bayesian Statistical Inference I 49 min · Video
  22. Lecture 22: Bayesian Statistical Inference II 53 min · Video
  23. Lecture 23: Classical Statistical Inference I 50 min · Video
  24. Lecture 24: Classical Inference II 52 min · Video
  25. Lecture 25: Classical Inference III; Course Overview 53 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Electrical Engineering and Computer Science
Teacher
Prof. John Tsitsiklis
Term
Fall 2010
Level
Undergraduate
Language
English
Subjects
Mathematics, Computer science, Engineering
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. John Tsitsiklis. Probabilistic Systems Analysis and Applied Probability. Fall 2010. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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