Lecture D2 (2026-09-22): Probabilistic Models

In this lecture, we review basic probability fundamentals (measure spaces, probability measures, random variables, probability density functions, probability mass functions, cumulative distribution functions, moments, mean/expected value/center of mass, standard deviation, variance), and then we start to build a vocabulary of different probabilistic models that are used in different modeling contexts. These include uniform, triangular, normal, exponential, Erlang-k, Weibull, and Poisson variables. We will finish the discussing next time with the Bernoulli-based discrete variables and Poisson processes. Interactive widgets referenced or related to this lecture: Probability Distribution Gallery Input Analyzer Pseudo-Random Number Generator Explorer