Grinstead and Snell's Introduction to Probability (Chapter 6: Expected Value and Variance)
by Charles M. Grinstead, J. Laurie Snell · Dartmouth College / American Mathematical Society (CHANCE Project)
Free 500-page probability textbook released under the GNU Free Documentation License. Chapter 6, Expected Value and Variance, covers expectation for discrete and continuous random variables, linearity, and historical problems including the St. Petersburg paradox, with exercises.
More resources on Expected Value
probabilitycourse.com
ProbabilityCourse.com is an online learning resource that provides a structured probability course with clear explanations, worked examples, and practice problems covering topics from basics to advanced theory.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Khan Academy Expected Value
Free lesson from Khan Academy's statistics and probability course combining short videos and practice exercises on the expected value of discrete random variables. Learners compute a distribution's mean from its probability table and interpret expected value in simple games and decisions.
Probabilistic Systems Analysis and Applied Probability (MIT 6.041SC)
Modeling and analysis of uncertainty: probability models, discrete and continuous random variables, Bayesian inference, limit theorems and random processes. Designed for independent study, with lecture videos, slides, recitation and tutorial problems, problem sets and exams with solutions, and TA problem-solving videos.
Lecture 5: Discrete Random Variables; Probability Mass Functions; Expectations (MIT 6.041SC)
Defines discrete random variables and their probability mass functions, including binomial and geometric examples, then introduces expected value and the expected value rule. The recorded lecture prepares learners to compute expectations for common discrete distributions and functions of random variables.
Expected Value — Statlect
Reference lecture defining expected value three ways: the discrete sum, the continuous integral, and the general Riemann-Stieltjes and Lebesgue formulations. Covers linearity, scaling, existence conditions for non-integrable variables, and solved exercises.