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  MA1254RANDOM PROCESSES3 1 0 100AIMThis 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.OBJECTIVESAt 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 VARIABLE9 +3Axioms 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 IISTANDARD DISTRIBUTIONS9 +3Binomial, Poisson, Geometric, Negative Binomial, Uniform, Exponential, Gamma, Weibull and Normal distributions and their properties - Functions of a random variable.UNIT III TWO DIMENSIONAL RANDOM VARIABLES9 + 3Joint distributions - Marginal and conditional distributions   Covariance - Correlation and regression - Transformation of random variables - Central limit theorem.UNIT IV CLASSIFICATION OF RANDOM PROCESSES9 + 3Definition 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 DENSITIES9 + 3Auto 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 : 60TEXT BOOKS 1.Ross, S.,  A First Course in Probability  , Fifth edition, Pearson Education, Delhi, 2002.2.Peebles Jr. P.Z.,  Probability Random Variables and Random Signal Principles  , Tata McGraw-Hill Pubishers, Fourth Edition, New Delhi, 2002. (Chapters 6, 7 a  nd 8).REFERENCES 1.Henry Stark and John W. Woods  Probability and Random Processes with Applications to Signal Processing  , Pearson Education, Third edition, Delhi, 2002.2.Veerarajan. T.,  Probabilitiy, Statistics and Random process  , Tata McGraw-Hill Publications, Second Edition, New Delhi, 2002.3.Ochi, M.K. ,  Applied Probability and Stochastic Process  , John Wiley & Sons, New York, 1990.
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