MA2261 PROBABILITY AND RANDOM PROCESSES SYLLABUS

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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

16

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), 3rd 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.