Course Archives    Theoretical Statistics and Mathematics Unit

Course: Probability Theory II Level: Undergraduate Time: Currently not offered

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: Midterm Exam marks Assignment marks Final Exam marks Total 100 marks Top of the page Past Exams

Midterm 06.pdf 07.pdf 08.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 14.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf 20.pdf Solution 10.pdf 15.pdf Semestral 03.pdf 06.pdf 09.pdf 10.pdf 11.pdf 12.pdf 13.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf Supplementary and Back Paper 06.pdf 09.pdf 10.pdf 12.pdf 15.pdf 16.pdf 17.pdf 18.pdf 19.pdf Top of the page

[ Semester Schedule ][ Statmath Unit ] [Indian Statistical Institute]