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Graduate Courses 21-680
Topics in Probability
6 units

Convergence of random sequences: modes of convergence and relations among them; convergence under transformations; applications. Classical limit theorems: series of independent random variables; the strong law of large numbers; the central limit theorem; the law of the iterated logarithm; applications. Conditional expectation: expectation given a finite set of random variables; expectation as minimum mean squared error; conditional distributions; computational aspects. Martingales: fundamentals; stopping times; optional sampling theorems; martingale convergence theorems; Wald's identity; applications.