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MIT OpenCourseWare

Probabilistic Systems Analysis and Applied Probability

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 )

Instructor

Professor John Tsitsiklis.

Computer science

2012

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