Statistics 110: Probability (Harvard Univ.). Taught by Professor Joe Blitzstein, this course is an introduction to probability as a language and
set of tools for understanding statistics, science, risk, and randomness. The ideas and methods are useful in statistics, science, engineering, economics,
finance, and everyday life. Topics include the following. Basics: sample spaces and events, conditioning, Bayes' Theorem. Random variables and their distributions:
distributions, moment generating functions, expectation, variance, covariance, correlation, conditional expectation. Univariate distributions: Normal, t, Binomial,
Negative Binomial, Poisson, Beta, Gamma. Multivariate distributions: joint, conditional, and marginal distributions, independence, transformations, Multinomial,
Multivariate Normal. Limit theorems: law of large numbers, central limit theorem. Markov chains: transition probabilities, stationary distributions, reversibility,
convergence.
Lecture 28 - Inequalities
This lecture considers the sum of a random number of random variable, and introduces 4 useful inequalities: Cauchy-Schwarz, Jensen, Markov, and Chebyshev.