Advanced Probability Theory

Probability measures and their distribution functions. Random variable: properties of mathematical expectation, independence, conditional probability and expectation. Convergence concepts: various modes of convergence of sequence of random variables; almost sure convergence, Borel-Cantelli Lemma, uniform integrability, convergence of moments. Weak and strong law of large numbers. Convergence in distribution, characteristic function: general properties, convolution, uniqueness and inversion, Lindeberg conditions and central limit theorem. This module is targeted at students who are interested in Statistics and are able to meet the pre-requisites.

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