18.440  Probability & Random Variables

This course introduces the mathematical framework of probability and random variables. It aims to provide a rigorous axiomatic development of the theory while, at the same time, building intuition and problem solving skills.
 
Some of the topics that we shall cover include: probability spaces; discrete and continuous random variables; distribution functions; conditional probabilities; Bayes' rule; joint distributions; expectations, variances, and higher moments; uniform, binomial, geometric, Poisson, exponential and Gaussian distributions; Markov, Chebyshev, and Chernoff inequalities; the law of large numbers and the central limit theorem; Markov chains; and the probabilistic method.