**Table of Contents**

Lecture 1: sample spaces, naive definition of probability, counting, sampling

Lecture 2: Bose-Einstein, story proofs, Vandermonde identity, axioms of probability

Lecture 3: birthday problem, properties of probability, inclusion-exclusion, matching problem

Lecture 4: independence, Newton-Pepys, conditional probability, Bayes’ rule

Lecture 5: law of total probability, conditional probability examples, conditional independence

Lecture 6: Monty Hall problem, Simpson’s paradox

Lecture 7: gambler’s ruin, first step analysis, random variables, Bernoulli, Binomial

Lecture 8: random variables, CDFs, PMFs, Hypergeometric

Lecture 10: linearity, Putnam problem, Negative Binomial, St. Petersburg paradox

Lecture 11: sympathetic magic, Poisson distribution, Poisson approximation

Lecture 12: discrete vs. continuous, PDFs, variance, standard deviation, Uniform, universality

Lecture 13: standard Normal, Normal normalizing constant

Lecture 14: Normal distribution, standardization, LOTUS

Lecture 15: midterm review, extra examples

Lecture 16: Exponential distribution, memoryless property

Lecture 17: moment generating functions (MGFs), hybrid Bayes’ rule, Laplace’s rule of succession

Lecture 18: MGFs to get moments of Expo and Normal, sums of Poissons, joint distributions

Lecture 19: joint, conditional, and marginal distributions, 2-D LOTUS, chicken-egg

Lecture 20: expected distance between Normals, Multinomial, Cauchy

Lecture 21: covariance, correlation, variance of a sum, variance of Hypergeometric

Lecture 22: transformations, LogNormal, convolutions, the probabilistic method

Lecture 23: Beta distribution, Bayes’ billiards, finance preview and examples

Lecture 24: Gamma distribution, Poisson processes

Lecture 27: conditional expectation (cont.), taking out what’s known, Adam’s law, Eve’s law

Lecture 29: law of large numbers, central limit theorem

Lecture 30: Chi-Square, Student-t, Multivariate Normal

Lecture 31: Markov chains, transition matrix, stationary distribution

Lecture 33: Markov chains (cont.), Google PageRank as a Markov chain