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