## March 6, 2010

### MA1254 Random Process

ANNA UNIVERSITY CHENNAI :: CHENNAI 600 025
CURRICULUM 2004
B.E. ELECTRONICS AND COMMUNICATION ENGINEERING

MA1254 Random Process 100

AIM
This course aims at providing the necessary basic concepts in random processes. A knowledge of fundamentals and applications of phenomena will greatly help in the understanding of topics such a estimation and detection, pattern recognition, voice and image processing networking and queuing.

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 PROBABILITY AND RANDOM VARIABLE 9 +3
Axioms of probability - Conditional probability - Total probability – Baye’s theorem - Random variable - Probability mass function - Probability density functions- Properties –Moments - Moment generating functions and their properties.

UNIT II STANDARD DISTRIBUTIONS 9 +3
Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.
UNIT III TWO DIMENSIONAL RANDOM VARIABLES 9 + 3
Joint distributions - Marginal and conditional distributions – Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.
UNIT IV 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.
UNIT V 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 - Linear time invariant system - System transfer function –Linear systems with random inputs – Auto correlation and cross correlation functions of input and output.

TUTORIAL 15

TOTAL : 60
TEXT BOOKS

• Ross, S., “A First Course in Probability”, Fifth edition, Pearson Education, Delhi, 2002.
• Peebles Jr. P.Z., “Probability Random Variables and Random Signal Principles”, Tata McGraw-Hill Pubishers, Fourth Edition, New Delhi, 2002. (Chapters 6, 7 and 8).

REFERENCES

• Henry Stark and John W. Woods “Probability and Random Processes with Applications to Signal Processing”, Pearson Education, Third edition, Delhi, 2002.
• Veerarajan. T., “Probabilitiy, Statistics and Random process”, Tata McGraw-Hill Publications, Second Edition, New Delhi, 2002.
• Ochi, M.K. , “Applied Probability and Stochastic Process”, John Wiley & Sons, New York, 1990.

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