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Graduate Courses 21-679
Foundations of Probability
6 units

Probability spaces: random experiments; sets and classes of sets; conditional probability. Random variables: operations/transformations of random variables, distributions and distribution functions; transforms of random variables and vectors. Independence: criteria for independence; functions of independent random variables; independent events; applications to occupancy problems and stochastic processes. Expectation: fundamental properties; integrals with respect to distribution functions; computation of expectations; moments of random variables and vectors; stochastic inequalities.