Joe Blitzstein (Professor of the Practice in Statistics and Co-Director of Undergraduate Studies in Statistics, Harvard University) has taught Statistics 110: Probability at Harvard each year since 2006. The on-campus Stat 110 course has grown from 80 students to over 300 students per year in that time. The lecture videos are available on iTunes U and YouTube. Stat 110 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. The prerequisites are calculus (mainly single variable) and familiarity with matrices.
The Lasting Lure of Logic (Harvard Gazette)