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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. IfXcan take on only whole numbers, between 0 and 23, (the hour of a day)thenXis a discrete random variable with a finite population.

Probability Distributions 3 2 Statistics of random variables The expected or mean value of a continuous random variable Xwith PDF f X(x) is the centroid of the probability density. µ X = E[X] = Z ∞ −∞ xf X(x) dx The expected value of an arbitrary function of X, …

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