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# Download ST5214 Advanced Probability Theory (Sem 1:2009/10) References

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ST5214 Advanced Probability Theory (Sem 1:2009/10) References Probability: Theory and Examples by Durrett, Duxbury Press (main text) Convergence of Stochastic Processes by Pollard, Springer An Introduction to Probability Theory and its Applications by Feller, Wiley Probability and Measure by Billingsley, Wiley Grading 50% Graded Homework Assignments 50% Final Exam Exam format Open book (with restrictions) Prerequisite ST2131 or Departmental Approval Course contents 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.