MA2261 PROBABILITY AND RANDOM PROCESSES L T P C
(Common to ECE & Bio Medical Engineering) 3 1 0 4
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.
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
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
Be able to analyze the response of random inputs to linear time invariant
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
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
LECTURES : 45 TUTORIAL : 15 TOTAL : 60 PERIODS
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).
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.