PROBABILITY THEORY & RANDOM PROCESS

Credits	Periods			Exam Hrs.	Sessional Marks	Exam Marks	Total Marks
	Theory	Tutorial	Lab
4	3	1	-	3	30	70	100

Probability Theory

Definitions of Probability, Axioms of Probability, Probability Spaces, Properties of Probabilities, Joint and Conditional Probabilities, Independent Events.

Random Variables

Probability Distribution Functions, Probability Density Functions, Joint Distribution of Two Variables, Conditional Probability Distribution and Density, Independent Random Variables.

Statistical Averages

Functions of Random Variables and Random Vectors, Statistical Averages, Characteristic Function of Random Variables, Inequalities of Chebyshev and Schwartz, Convergence Concepts, Central Limit Theorem.

Random Processes

Stationarity, Ergoridicity, Covariance Function and their Properties, Spectral Representation, Weiner-Kinchine Theorem, Linear operations, Gaussian Function, Poisson Processes, Low-pass and Band-pass Noise Representation.

Textbook :

1.      Probability Theory and Random Processes, S. P. Eugene Xavier, S. Chand and Co. New Delhi, 1998 (2^nd Edition).

2.      Probability Theory and Random Signal Principles, Peebles, Tata McGrew Hill Publishers.

References :

1.      Signal Analysis, Papoulis, McGraw Hill N. Y., 1977.

2.      Introduction to Random Signals and Noise, Davenport W. B. Jrs. and W. I. Root, McGraw Hill N.Y., 1954.