Probability Theory

Code: MA683 | L-T-P-C: 3-1-0-8

MA683 Probability Theory [3-1-0-8] Prerequisite: Nil

Probability spaces, probability measures on countable and uncountable spaces, conditional probability, independence; Random variables and vectors, distribution functions, functions of random vectors, standard univariate and multivariate discrete and continuous distributions and their properties; Mathematical expectations, moments, moment generating functions, characteristic functions, inequalities, conditional expectations, covariance, correlation; Modes of convergence of sequences of random variables, weak and strong laws of large numbers, central limit theorems; Introduction to stochastic processes, definitions and examples, Markov chains, Poisson processes, Brownian motion.

Texts/References:

1. J. Jacod and P. Protter, Probability Essentials, Springer, 2004.
2. S. Ross, A First Course in Probability, 6th edition, Pearson, 2002.
3. G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, 3rd edition, Oxford University Press, 2001.
4. J. Rosenthal, A First Look at Rigorous Probability Theory, 2nd edition, World Scientific, 2006.
5. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
6. V. K. Rohatgi and A. K. Md. E. Saleh, An Introduction to Probability and Statistics, 2nd edition, Wiley, 2001.
7. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Edition, Wiley, 1968.