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Probability Distributions - Duke University

Probability DistributionsCEE 201L. Uncertainty, Design, and OptimizationDepartment of Civil and Environmental EngineeringDuke UniversityPhilip Scott Harvey, Henri P. Gavin and Jeffrey T. ScruggsSpring 2022In the context of random variables, capital italics (X) represent an uncertain quantity (a randomvariable) and lower case italics (x) represent a particular value of that random variable. Randomvariables can bediscreteorcontinuous. Discreterandom variables can take on values that are members of a (finite or infinite) setof discrete values. IfXcan take on only positive whole numbers (the number of times ateam can win over all time), thenXis a discrete random variable with an infinitely largepopulation.

1E.J. Gumbel, Statistics of extremes, Columbia Univ Press, 1958 Lasse Makkonen, “Problems in the extreme value analysis,” Structural Safety 2008:30:405-419 (CC) BY-NC-ND February 14, 2022 PSH, HPG, JTS

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