Probability and Random Variables: Classical and statistical definitions of probability and their defects. Sample space, sigma algebra of events, probability, conditional probability and Bayes' theorem.

Random Variables: Distribution functions, continuous random variables, probability density function, multivariate distributions, marginal and conditional distributions.

Mathematical Expectations: Moments, variance, convariance, standard deviation, moment generating function, product moments, conditional expectations.

Some special probability distributions and densities: Discreate, Bernoulli, Binomial, Poisson, Uniform, Gamma and amp; Normal distributions and their properties.

Functions of Random variables: Distribution function technique, transformation technique, moment generating function technique.

Sequence of random variables: Stochastic convergence and limit theorems, characteristic functions, convergence, law of large numbers, central limit theorem.

Linear regression and correlation, method of least square, multiple linear regression

Random process, Markov process, stationary processes, first order and second order properties, Auto correlation and Auto covariance, Guassian process, Martingles, Random walk.

Texts / References Books:
1. G.P. Beaumont, Probability and random variables, John Wiley and sons.
2. A. Papoulis, and S. Unnikrishna Pillai: Probability, Random Variables and Stochastic Processes, 4th Edn., Tata McGraw Hill, 2002.
3. P.G. Hoel, S.C. Port, and C.J. Stone: Introduction to Probability Theory, Universal Book Stall, 2000.
4. J. Medhi: Stochastic Processes, New Age International, 1994.

[We will use Hoel-Port-Stone for Probability part and Trivedi for the Stochastic Processes part].