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MATH 524 Probability Theory 3 Credits
Semi-algebras and sigma-algebras of events, Kolmogorov?s axioms of probability, consequences thereof, probability spaces, measurability, random variables as measurable mappings, random vectors, probability measures induced on Borel sigma-algebras by random vectors, distributions and distribution functions, extension of probability measure starting by semi-algebras, mathematical expectation, expected values of non-negative simple, non-negative and general random variables, properties, conditional distributions and independence, Borel-Cantelli lemma, conditional expectation given a sub sigma-algebra, Radon-Nikodym theorem, different modes of convergence, almost sure convergence, convergence in probability, convergence in L^p, convergence in distribution, different implications between them, characteristic functions, inversion formulas, relation to convergence concepts, the weak and the strong law of large numbers, central limit theorem.
Last Offered Terms Course Name SU Credit
Spring 2018-2019 Probability Theory 3
Fall 2017-2018 Probability Theory 3
Fall 2010-2011 Probability Theory 3
Fall 2009-2010 Probability Theory 3
Prerequisite: __
Corequisite: __
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year)
General Requirements: