Probabilistic Systems Analysis and Applied Probability

Video Lectures

Lecture 1: Probability Models and Axioms

Lecture 2: Conditioning and Bayes' Rule

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

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