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).
Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic
Thursday, September 16, 2021
Lecture D1 (2021-09-16): Probability and Random Variables
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