Lecture D1 (2026-09-17): Probability and Random Variables
from IEE 475: Simulating Stochastic Systems Hosted by Theodore P. Pavlic
In this lecture, we introduce the measure-theoretic concept of a random variable (which is neither random nor a variable) and related terms, such as outcomes, events, probability measures, moments, means, etc. Throughout the lecture, we use the metaphor of probability as mass (and thus probability density as mass density, and a mean as a center of mass). This allows us to discuss the "statistical leverage" of outliers in a distribution (i.e., although they happen infrequently, they still have the ability to shift the mean significantly, as in physical leverage). This sets us up to talk about random processes and particular random variables in the next lecture. Concept Explorers linked from this lecture: Concept Explorer: Pseudo-Random Number Generators and AI Watermarking Concept Explorer: Monte Carlo Examples for Stochastic Modeling Concept Explorer: Input Modeling (fully functional Input Analyzer) Concept Explorer: Probability Distributions for Input Modeling and Statistics
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