PROBABILITY THEORY AND RANDOM PROCESSES

Code: MA225 | L-T-P-C: 3-1-0-8

Probability spaces, independence, conditional probability, and basic formulae; Random variables, distribution functions, probability mass/density functions, functions of random variables; Standard univariate discrete and continuous distributions and their properties; Mathematical expectations, moments, moment generating functions, characteristic functions; Random vectors, multivariate distributions, marginal and conditional distributions, conditional expectations; Modes of convergence of sequences of random variables, laws of large numbers, central limit theorem; Definition and classification of random processes, discrete-time Markov chains, classification of states, limiting and stationary distributions, Poisson process, continuous-time Markov chains.

Texts:

1. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2000.
2. G. R. Grimmett and D. R. Stirzaker, Probability and Random Processes, 3rd Ed., Oxford University Press, 2001.

References:

1. S. M. Ross, Introduction to Probability Models, 11th Ed., Academic Press, 2014.
2. J. Medhi, Stochastic Processes, 3rd Ed., New Age International, 2009.
3. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968.
4. K. S. Trivedi, Probability and Statistics with Reliability, Queuing, and Computer Science Applications, 2nd Ed., Wiley, 2001.
5. C. M. Grinstead and J. L. Snell, Introduction to Probability, 2nd Ed., Universities Press India, 2009