Basic definition of probability, Random variables, Probability density function, Probability distribution function, Standard univariate and multivariate distributions, Conditional distributions and densities, Moment generating functions, Characteristic functions, Limit theorems.
Point estimation, Interval estimation, Hypothesis testing, Simple linear regression, Correlation.
Random Processes, Markov Processes,
Stationary processes, Ergodicity, Auto correlation, Cross
correlation, Power spectral density.
Textbook: (that I will be following for the probability and
V.K. Rohatgi, and A.K. Md. Ehsanes Saleh: An Introduction to Probability and Statistics, 2nd Edn., Wiley, 2000.
Other Texts and References:
1. A. Papoulis, and S. Unnikrishna Pillai: Probability, Random Variables and Stochastic Processes, 4th Edn., Tata McGraw Hill, 2002.
2. H. J. Larson: Introduction to Probability Theory and Statistical Inference, 3rd edition, Wiley, 1969.
3. H. Stark, and J. W. Woods: Probability, Random Processes and Estimation Theory for Engineers, Prentice Hall, 1986.
4. P.G. Hoel, S.C. Port, and C.J. Stone: Introduction to Probability Theory, Universal Book Stall, 2000.
5. J. Medhi: Stochastic Processes, New Age International, 1994.
6. S.M. Ross: Stochastic Processes, 2nd Edn., John Wiley, 1995.