Lecture D1 (2020-09-17): Probability and Random Variables

In this lecture, we introduce basic concepts from probability theory that will be useful as we move toward input modeling for Discrete Event System simulation modeling. Our introduction starts with a brief acknowledgment of measure theory and then a definition of random variables, sample spaces, events, and probability measures. We cover the discrete random variable, the continuous random variable, and the related probability mass and probability density functions. We pivot to discuss cumulative distribution functions and several applications of moments (expected value, mean, variance, standard deviation, etc.). Throughout the lecture, we use the analogy of probability as a kind of weight of a set of mutually exclusive outcomes.