infocobuild

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.