PROBABILITY AND RANDOM VARIABLES
Probability – Axioms of probability – Conditional probability – Baye‘s theorem - Discrete and continuous random variables – Moments – Moment generating functions – Binomial, Poisson, Geometric, Uniform, Exponential and Normal distributions.
TWO - DIMENSIONAL RANDOM VARIABLES
Joint distributions – Marginal and conditional distributions – Covariance – Correlation and linear regression – Transformation of random variables – Central limit theorem (for independent and identically distributed random variables).
Classification – Stationary process – Markov process - Markov chain - Poisson process – Random telegraph process.
CORRELATION AND SPECTRAL DENSITIES
Auto correlation functions – Cross correlation functions – Properties – Power spectral density –Cross spectral density – Properties.
LINEAR SYSTEMS WITH RANDOM INPUTS
Linear time invariant system – System transfer function – Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.
Reference Book:
1. Cooper. G.R., McGillem. C.D., "Probabilistic Methods of Signal and System
Analysis", Oxford University Press, New Delhi, 3rd Indian Edition, 2012.
2. Hwei Hsu, "Schaum‘s Outline of Theory and Problems of Probability, Random
Variables and Random Processes ", Tata McGraw Hill Edition, New Delhi, 2004.
3. Miller. S.L. and Childers. D.G., ―Probability and Random Processes with
Applications to Signal Processing and Communications ", Academic Press,
2004.
4. Stark. H. and Woods. J.W., ―Probability and Random Processes with
Applications to Signal Processing ", Pearson Education, Asia, 3rd Edition, 2002.
5. Yates. R.D. and Goodman. D.J., ―Probability and Stochastic Processes", Wiley
India Pvt. Ltd., Bangalore, 2nd Edition, 2012.
Text Book:
1. Ibe, O.C.," Fundamentals of Applied Probability and Random Processes ", 1
Indian Reprint,Elsevier, 2007.
2. Peebles, P.Z., "Probability, Random Variables and Random Signal Principles ",
Tata McGraw Hill, 4th Edition, New Delhi, 2002.
