Lecture D1 (2021-09-16): Probability and Random Variables

In this lecture, we use motivation from stochastic modeling (i.e., incorporating randomness into models in order to capture realistic variation without having to specify a great many details) to formally introduce random variables and probability spaces (as a subset of measure theory). We heavily lean on the analogy between probability and mass as we introduce the sample space, probability measure, random variable, probability mass function (pmf), probability density function (pdf), cumulative distribution function (cdf), and moments (including expectation and central moments as in variance).