MA2261 PROBABILITY AND RANDOM PROCESSES 3 1 0 4
(Common to ECE & Bio Medical Engineering)
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 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
- Oliver C. Ibe, “Fundamentals of Applied probability and Random processes”, Elsevier, First Indian Reprint ( 2007) (For units 1 and 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).