2K6 EC 705 (A): PROBABILITY AND RANDOM PROCESS

Module I: (13 hours)
Axioms of probability – Conditional probability – Total probability – Baye’s theorem – Random variable – Probability mass function – Probability density functions – Properties –Moments – Moment generating functions and their properties
Module II: (14 hours)
Binomial – Poisson – Uniform – Exponential – Gamma – Normal distributions and their properties – Functions of a random variable – Chebyshev Inequality.
Module III: (13 hours)
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and regression – Transformation of random variables – Central limit theorem.
Module IV: (12 hours)
Definition and examples – first order – second order – strictly stationary – wide – sense stationary and Ergodic processes – Markov process – Binomial – Poisson and Normal processes – Sine wave process.

TEXT BOOKS
1. Ross S., “A First Course in Probability”, Seventh Edition , Pearson Education, 2006.
2. S.Karlin and H.M. Taylor, “An Introduction to Stochastic Modeling”, Academic Press, 2007.
Reference books
1. Veerarajan T., “Probabilitiy – Statistics and Random process”, Second Edition , Tata McGraw–Hill, 2006.
2. Richard A Johnson, “Probability and Statistics for Engineers” Seventh Edition , Pearson Education, 2005.
3. Mood, Alexander McFarlane, “Introduction to Theory of Statistics”, Tata McGraw – Hill,1974.