Syllabus for PROBABILITY AND RANDOM PROCESSES

UNIT I                              RANDOM VARIABLES
Discrete and Continuous random variables - Moments - Moment generating functions - Binomial, Poisson, Geometric, Uniform, Exponential, Gamma, Weibull and Normal distributions - Functions of a random variable

UNIT II                 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).

UNIT III              RANDOM PROCESSES
Classification - Stationary process - Markov process - Poisson process - Random telegraph process.

UNIT IV            CORRELATION AND SPECTRAL DENSITIES

Auto-correlation functions - Cross-correlation functions - Properties - Power spectral density - Cross-spectral density - Properties.

UNIT V             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 - White noise.

L: 45, T: 15,
Total : 60
TEXT BOOKS

1. Ibe, O.C.,“Fundamentals of Applied Probability and Random Processes”, Elsevier, 1st Indian Reprint, (2007).
 
2. Peebles, P.Z., “Probability, Random Variables and Random Signal Principles”, Tata McGraw Hill, 4th edition, New Delhi, (2002).

REFERENCES

1. Yates, R.D. and Goodman, D.J., “Probability and Stochastic Processes”, John Wiley and Sons, 2nd edition, (2005).

2. Stark, H. and Woods, J.W., “Probability and Random Processes with Applications to Signal Processing”, Pearson Education, Asia, 3rd edition, (2002).

3. Miller, S.L. and Childers, D.G.,“Probability and Random Processes with Applications to Signal Processing and Communications”, Academic Press, (2004).

4. Hwei Hsu, “Schaum’s Outline of Theory and Problems of Probability, Random Variables and Random Processes”, Tata McGraw Hill edition, New Delhi, (2004).