| Course Archives Theoretical Statistics and Mathematics Unit | |
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Course: Basic Probability Theory Time: Currently not offered Level: Postgraduate |
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| Syllabus
Past Exams Syllabus: Orientation. Combinatorial probability. Fluctuations in Coin Tossing and Random Walks.Combination of Events, Occupancy and Matching Problems. Conditional probabilities. UrnModels. Independence. Random Variables, discrete distributions, Expectation, variance and moments, probability gen-erating functions and moment generating functions, Tchebychevs inequality. Standard discretedistributions: uniform, binomial, Poisson, geometric, hypergeometric, negative binomial. Con-tinuous random variables: univariate densities and distributions, Expectations, variance andmoments, standard univariate densities: normal, exponential, gamma, beta, chi-square, Cauchy. Joint and conditional distributions, Independence of random variables, Transformation of variables. Laws of Large Numbers (proofs optional). Suggested Texts : 1. S. Ross, First course in probability theory, Mac Millan (1989). 2. P.G. Hoel, S.C. Port and C.J. Stone, Introduction to Probability Theory, Universal BookStall, New Delhi (1991). 3. W.Feller, An introduction to probability theory and its applications Vol 1, Wiley (1950). 4. K.L. Chung, Elementary Probability Theory, Springer (Indian reprint 2003). Top of the page Past Exams | |
Midterm
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[ Semester Schedule ] [ SMU ] [Indian Statistical Institute] |