RANDOM VARIABLE AND PROBABILITY DISTRIBUTIONS
Probability – Axioms of probability-– Conditional probability – Baye‘s theorem- Discrete and Continuous Random Variables – Moments – Moment generating functions–Binomial, Poisson, Exponential and Normal distributions.
TWO DIMENSIONAL RANDOM VARIABLES
Joint distributions –Marginal and conditional distributions – Covariance –Correlation and Regression- Transformation of random variables.
CLASSIFICATION OF RANDOM PROCESSES
Random Process – Stationary Process - Wide-sense stationary and Ergodic processes - Markov process – Markov Chain- Poisson Process.
CORRELATION AND SPECTRAL DENSITIES
Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density – Properties-Wiener-Khintchine relation.
LINEAR SYSTEMS WITH RANDOM INPUTS
Linear time invariant system- System transfer function –Linear system with random inputs –Auto correlation and Cross correlation functions of input and output.
Reference Book:
1.Cooper. G.R.andMcGillem. C.D., "Probabilistic Methods of Signal and System Analysis", 3rd Indian Edition, Oxford University Press, New Delhi, 2012. (UNIT-I,II,III,IV,V)
2.Yates. R.D. and Goodman.D.J., "Probability and Stochastic Processes", 2nd Edition, Wiley India Pvt. Ltd., Bangalore, 2012. (UNIT-I,II,III)
3. Leon-Garcia, A, “Probability and Random Processes for Electrical Engineering”, Pearson Education Asia, Second Edition, 2007. (UNIT-I,II,III,IV)
Text Book:
1.Oliver C. Ibe, “Fundamentals of Applied probability and Random processes”, Elsevier, First Indian Reprint (2014) (UNIT-I,II,III).
2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, TataMcGraw-Hill Publishers, Fourth Edition, New Delhi, 2002. (UNIT-III,IV,V).
