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

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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
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
Supplementary and Back Paper
06.pdf 09.pdf 10.pdf 12.pdf 15.pdf 16.pdf 17.pdf

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