Probabilistic System Analysis and Applied Probability (Fall 2010) (M-I-T)

Lecture 1 Probability Models and Axioms

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 2 Conditioning and Bayes’ Rule

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

Lecture 3 Independence

Lecture 4 Counting

Lecture 5 Discrete Random Variables; Probability Mass Functions; Expectations

Lecture 6 Discrete Random Variable Examples; Joint PMFs

Lecture 7 Multiple Discrete Random Variables Expectations, Conditioning, Independence

Lecture 8 Continuous Random Variables

Lecture 9 Multiple Continuous Random Variables