MA 225 |
PROBABILITY THEORY AND RANDOM PROCESSES |
3-1-0-8 |
Prerequistes: Nil Syllabus: 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. Textbooks: 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. |