MIT 6.041 Probabilistic Systems Analysis and Applied Probability
- 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
- 11. Probability Models and Axioms
- 22. Conditioning and Bayes' Rule
- 33. Independence
- 44. Counting
- 55. Discrete Random Variables I
- 66. Discrete Random Variables II
- 77. Discrete Random Variables III
- 88. Continuous Random Variables
- 99. Multiple Continuous Random Variables
- 1010. Continuous Bayes' Rule; Derived Distributions
- 1111. Derived Distributions (ctd.); Covariance
- 1212. Iterated Expectations
- 1313. Bernoulli Process
- 1414. Poisson Process I
- 1515. Poisson Process II
What to take next
Related courses
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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