MA2261 PROBABILITY AND RANDOM PROCESSES

MA2261                       PROBABILITY AND RANDOM PROCESSES               3   1   0   4

                                    (Common to ECE & Bio Medical Engineering)

                                                                                                                          

AIM

This course aims at providing the necessary basic concepts in random processes.    Knowledge of fundamentals and applications of random phenomena will greatly help in the understanding of topics such as signals & systems, pattern recognition, voice and image processing and filtering theory.

OBJECTIVES

At the end of the course, the students would

·                 Have a fundamental knowledge of the basic probability concepts.

·                 Have a well-founded knowledge of standard distributions which can describe real    life phenomena.

·                 Acquire skills in handling situations involving more than one random variable and  functions of random variables.

·                 Understand and characterize phenomena which evolve with respect to time in  probabilistic manner.

·                 Be able to analyze the response of random inputs to linear time invariant systems.

UNIT I              RANDOM VARIABLES                                                                                    9 + 3

Discrete and continuous random variables – Moments - Moment generating functions and their properties. Binomial, Poisson ,Geometric, Uniform, Exponential, Gamma and normal  distributions – Function of Random Variable.

UNIT II               TWO DIMENSIONAL RANDOM VARIBLES                                               9 + 3

Joint distributions - Marginal and conditional distributions – Covariance - Correlation and Regression - Transformation of random variables - Central limit theorem (for iid random variables)

UNIT III    Classification of RANDOM PROCESSES                                                   9 + 3

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 – Random telegraph process.

UNIT IV   Correlation and spectral densities                                         9 + 3

Auto correlation - Cross correlation - Properties – Power spectral density – Cross spectral density - Properties – Wiener-Khintchine relation – Relationship between cross power spectrum and cross correlation function

UNIT V    LINEAR SYSTEMS WITH RANDOM INPUTS                                           9 + 3

Linear time invariant system - System transfer function – Linear systems with random inputs – Auto correlation and cross correlation functions of input and output – white noise.

          LECTURES : 45        TUTORIAL : 15       TOTAL : 60 PERIODS 

TEXT BOOKS

1. Oliver C. Ibe,  “Fundamentals of Applied probability and Random processes”, Elsevier, First Indian Reprint ( 2007)  (For units 1 and 2)

2. Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, Tata McGraw-Hill Publishers, Fourth Edition, New Delhi, 2002. (For units 3, 4 and 5).

REFERENCES

1.      Miller,S.L and Childers, S.L, “Probability and Random Processes with applications to Signal Processing and Communications”, Elsevier Inc., First Indian Reprint 2007.

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

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

4.      Leon-Garcia,A, “Probability and Random Processes for Electrical Engineering”, Pearson Education Asia, Second Edition, 2007.

5.      Yates and D.J. Goodman, “Probability and   Stochastic Processes”, John Wiley and Sons, Second edition, 2005.