Lecture 1Lecture Overview

Prev1 / 265Next

Lecture 1: Probability Models and Axioms

Lecture Overview

Sample Space

Sample Space Examples

Probability Axioms

Simple Properties of Probabilities

More Properties of Probabilities

A Discrete Example

A Continuous Example

Countable Additivity

Interpretations & Uses of Probabilities

Supplement: Mathematical Background

Lecture 2: Conditioning and Bayes' Rule

Lecture 3: Independence

Lecture 4: Counting

Lecture 5: Discrete Random Variables

Supplement: Functions

Lecture 6: Variance; Conditioning on an Event; Multiple R.V.s

Lecture 7: Conditioning on a Random Variable; Independence

Supplement: Independence Topics

Lecture 8: Continuous Random Variables

Lecture 9: Further Topics on Continuous Random Variables

Supplement: Buffon's Needle & Monte Carlo Simulation

Lecture 10: Conditional PDFs and Bayes' Rule

Lecture 11: Functions of Random Variables

Supplement: Simulation

Lecture 12: Sums of Random Variables, Covariance, and Correlation

Lecture 13: Conditional Expectation and Total Variance

Supplement: Conditional Expectation Properties

Lecture 14: Introduction to Bayesian Inference

Supplement: The Beta Formula

Lecture 15: Linear Models and Estimation

Lecture 16: Least Mean Squares Estimation

Lecture 17: Linear Least Mean Squares Estimation

Lecture 18: Inequalities, Convergence, and the Weak Law of Large Numbers

Supplement: Inequalities and Convergence

Lecture 19: The Central Limit Theorem

Lecture 20: An Introduction to Classical Statistics

Lecture 21: The Bernoulli Process

Lecture 22: The Poisson Process

Lecture 23: More on the Poisson Process

Supplement: Poisson Process Topics

Lecture 24: Markov Processes

Lecture 25: Markov Chains, Steady State, and Birth-Death Processes

Lecture 26: Markov Chains, Absorption, and Gambler's Ruin