MATH 450 Probability Theory
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Sample spaces, sigma algebras, probability measures, measurable sets and functions, random variables, independence, Borel-Cantelli Lemmas, expectation, Monotone convergence theorem, Fatou's lemma, dominated convergence theorem, modes of convergence, weak and strong law of large numbers, moment-generating and characteristic functions, Central Limit Theorem (CLT), Lindeberg-Feller CLT, conditional expectations, Martingales and Martingale Convergence Theorem.
Credit units: 3 ECTS Credit units: 5, Prerequisite:
MATH 213 and (MATH 230 or MATH 250 or MATH 255).
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