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MIT 6.041 Probabilistic Systems Analysis and Applied Probability

By MIT OpenCourseWare

Course audio
Course audio: English
Level
Intermediate
Length
15 lessons

What you'll be able to do

  • Build probability models and apply Bayes' rule
  • Work with discrete and continuous random variables
  • Understand the law of large numbers and central limit theorem

About this course

MIT's introductory probability course taught by Professor John Tsitsiklis. Lectures begin with probability models and axioms, conditioning and Bayes' rule, independence and counting, then cover discrete and continuous random variables, expectation and variance, joint distributions, derived distributions, the law of large numbers, the central limit theorem, Bayesian inference, and Markov chains. It suits engineering, CS and data science students who want solid probability before statistics or machine learning. Follow with Professor Leonard's Statistics or MIT 18.650.

Before you start: Single-variable calculus

Syllabus

Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube

  1. 11. Probability Models and Axioms
  2. 22. Conditioning and Bayes' Rule
  3. 33. Independence
  4. 44. Counting
  5. 55. Discrete Random Variables I
  6. 66. Discrete Random Variables II
  7. 77. Discrete Random Variables III
  8. 88. Continuous Random Variables
  9. 99. Multiple Continuous Random Variables
  10. 1010. Continuous Bayes' Rule; Derived Distributions
  11. 1111. Derived Distributions (ctd.); Covariance
  12. 1212. Iterated Expectations
  13. 1313. Bernoulli Process
  14. 1414. Poisson Process I
  15. 1515. Poisson Process II

What to take next

Videos by MIT OpenCourseWare, played from their official YouTube channel. Subscribe on YouTube

Licence: CC BY-NC-SA 4.0, MIT OpenCourseWare, ocw.mit.edu. Free for everyone, never sold.

Sabaq lists the first 15 videos of this playlist; the rest continue on YouTube. Full playlist on YouTube

Lessons last checked Oct 2026. Course summary and lesson structure by Sabaq.

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