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Course: Probability Theory II Instructor: D Yogeshwaran Room: G24 Level: Undergraduate Time: Currently offered |
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Syllabus Past Exams Syllabus Joint densities and distributions. Transformation of variables (assuming Jacobian formula). Distributions of sum, maxima, minima, order statistics, range etc. Multivariate normal (properties, linear combinations) and other standard multivariate distributions (discrete and continuous) as examples. Standard sampling distributions like t ;x^2 and F. Conditional distributions, Conditional Expectation. Characteristic functions: properties, illustrations, inversion formula, continuity theorem (without proof). Central Limit Theorem for i.i.d. case with finite variance. Elements of modes of convergence of random variables and the statement of the strong law of large numbers. Reference Texts : 1. K. L. Chung: Elementary Probability Theory 2. P. G. Hoel, S.C. Port and C.J. Stone : Introduction to Probability Theory 3. R. Ash : Basic Probability Theory 4. W. Feller : Introduction to Probability Theory and its Applications, Volume 1 5. W. Feller : Introduction to Probability Theory and its Applications, Volume 2 6. P. Billingsley : Probability and Measure 7. V.K.Rohatgi: Probability theory Evaluation:
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Midterm
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[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute] |