6.041/6.431 Probabilistic Systems Analysis and Applied Probability (Fall 2010, MIT OCW) | Computer Science

6.041 Probabilistic Systems Analysis and Applied Probability

6.041/6.431 Probabilistic Systems Analysis and Applied Probability (Fall 2010, MIT OCW). Instructor: Professor John Tsitsiklis. 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. The aim of this course is to introduce the relevant models, skills, and tools, by combining mathematics with conceptual understanding and intuition. (from ocw.mit.edu)

Probability Models and Axioms

Lecture 01 - Probability Models and Axioms

Lecture 02 - Conditioning and Bayes' Rule

Lecture 03 - Independence

Lecture 04 - Counting

Lecture 05 - Discrete Random Variables; Probability Mass Function; Expectations

Lecture 06 - Discrete Random Variable Examples; Joint PMFs

Lecture 07 - Multiple Discrete Random Variables; Expectations, Conditioning, Independence

Lecture 08 - Continuous Random Variables

Lecture 09 - Multiple Continuous Random Variables

Lecture 10 - Continuous Bayes' Rule; Derived Distributions

Lecture 11 - Derived Distributions; Convolution; Covariance and Correlation

Lecture 12 - Iterated Expectations; Sum of a Random Number of Random Variables

Lecture 13 - Bernoulli Process

Lecture 14 - Poisson Process I

Lecture 15 - Poisson Process II

Lecture 16 - Markov Chains I

Lecture 17 - Markov Chains II

Lecture 18 - Markov Chains III

Lecture 19 - Weak Law of Large Numbers

Lecture 20 - Central Limit Theorem

Lecture 21 - Bayesian Statistical Inference I

Lecture 22 - Bayesian Statistical Inference II

Lecture 23 - Classical Statistical Inference I

Lecture 24 - Classical Inference II

Lecture 25 - Classical Inference III; Course Overview

References

Probabilistic Systems Analysis and Applied Probability (Fall 2010)
Instructor: Professor John Tsitsiklis. Lecture Notes. Recitations. Assignments and Solutions. Exams and Solutions. Tutorials. A subject on the modeling and analysis of random phenomena and processes.