Lecture Notes

L1 Probability Models and Axioms (PDF)
L2 Conditioning and Bayes' Rule (PDF)
L3 Independence (PDF)
L4 Counting Sections (PDF)
L5 Discrete Random Variables; Probability Mass Functions; Expectations (PDF)
L6 Conditional Expectation; Examples (PDF)
L7 Multiple Discrete Random Variables (PDF)
L8 Continuous Random Variables - I (PDF)
L9 Continuous Random Variables - II (PDF)
L10 Continuous Random Variables and Derived Distributions (PDF)
L11 More on Continuous Random Variables, Derived Distributions, Convolution (PDF)
L12 Transforms (PDF)
L13 Iterated Expectations (PDF)
L13A Sum of a Random Number of Random Variables (PDF)
L14 Prediction; Covariance and Correlation (PDF)
L15 Weak Law of Large Numbers (PDF)
L16 Bernoulli Process (PDF)
L17 Poisson Process (PDF)
L18 Poisson Process Examples (PDF)
L19 Markov Chains - I (PDF)
L20 Markov Chains - II (PDF)
L21 Markov Chains - III (PDF)
L22 Central Limit Theorem (PDF)
L23 Central Limit Theorem (cont.), Strong Law of Large Numbers (PDF)