# Probabilistic Systems Analysis and Applied Probability

### Course Description

An 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.

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

John Tsitsiklis. 6.041 Probabilistic Systems Analysis and Applied Probability, Fall 2010. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 31 Jan, 2015). License: Creative Commons BY-NC-SA

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### Video Lectures & Study Materials

Visit the official course website for more study materials: http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-041-probabilistic-systems-analysis-and-applied-probability-fall-2010/index.htm

# Lecture Play Lecture Notes & Slides
1 Probability Models and Axioms (51:11) Play Video Lecture Notes
2 Conditioning and Bayes' Rule (51:11) Play Video Lecture Notes
3 Independence (46:30) Play Video Lecture Notes
4 Counting (51:35) Play Video Lecture Notes
5 Discrete Random Variables I (50:35) Play Video Lecture Notes
6 Discrete Random Variables II (50:53) Play Video Lecture Notes
7 Discrete Random Variables III (50:42) Play Video Lecture Notes
8 Continuous Random Variables (50:29) Play Video Lecture Notes
9 Multiple Continuous Random Variables (50:51) Play Video Lecture Notes
10 Continuous Bayes' Rule; Derived Distributions (48:53) Play Video Lecture Notes
11 Derived Distributions (ctd.); Covariance (51:55) Play Video Lecture Notes
12 Iterated Expectations (47:54) Play Video Lecture Notes
13 Bernoulli Process (50:58) Play Video Lecture Notes
14 Poisson Process I (52:44) Play Video Lecture Notes
15 Poisson Process II (49:28) Play Video Lecture Notes
16 Markov Chains I (52:06) Play Video Lecture Notes
17 Markov Chains II (51:25) Play Video Lecture Notes
18 Markov Chains III (51:50) Play Video Lecture Notes
19 Weak Law of Large Numbers (50:13) Play Video Lecture Notes
20 Central Limit Theorem (51:23) Play Video Lecture Notes
21 Bayesian Statistical Inference I (48:50) Play Video Lecture Notes
22 Bayesian Statistical Inference II (52:16) Play Video Lecture Notes
23 Classical Statistical Inference I (49:32) Play Video Lecture Notes
24 Classical Inference II (51:50) Play Video Lecture Notes
25 Classical Inference III (52:07) Play Video Lecture Notes