MA2261 - PROBABILITY AND RANDOM PROCESSES |
UNIT.1 RANDOM VARIABLES |
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.2 TWO DIMENSIONAL RANDOM VARIBLES |
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and
Regression - Transformation of random variables - Central limit theorem (for iid random
variables) |
UNIT.3CLASSIFICATION OF RANDOM PROCESSES |
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.4CORRELATION AND SPECTRAL DENSITIES |
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.5LINEAR 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. |
Text Book |
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. |
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