JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

UNIT - I

Stationary Random Processes from a Probability Point of View: Probability Density and Probability Distribution Functions of a Random Variable, Expected Value of Random Variable, Markov and Chebyshev Inequalities, Computer Methods for Generating Random Variables, Multidimensional Random variables, Chi-square tests of hypotheses concerning distribution.

UNIT - II

Random Processes Analyzed in the Time Domain: Continuous and Discrete Time, Stationarity, Auto Covariance and Auto Correlation functions, Continuity, differentiation, Integrals of Random Processes. Some special cases: The Poisson process, the Normal (Gaussian) Process.

UNIT - III

Random Processes Analyzed in the Frequency Domain: The Fourier Transform, Spectral Density, The Cross Power Spectral Density. Linear Systems with random input: Impulse response, Transfer function, the relation between the spectral density for the input and for the output

UNIT - IV

Markov Chains: Markov Processes: Discrete time Markov chains, state transition probability matrix, n-step state transition probability, transition diagrams, classification of states, limiting state probabilities, Continuous-time Markov chains, Gambler’s ruin as a Markov chains

UNIT - V

Basic Queuing Theory: Elements of a Queuing System, Little’s Formula, M/M/1, Queue- Delay Distribution in M/M/1 System, M/M/1 System with Finite Capacity, M/G/1 Queuing system- Residual Service Time, Mean Delay in M/G/1 Systems.

TEXT BOOKS:

• 1. Peebles, P. Z, “Probability, Random Variables, and Random Signal Principles”, 1993 3rd Edition, New York, McGraw-Hill
• 2. Oliver C. Ibe, “Fundamentals of Applied Probability and Random Processes”, Elsevier, 2009 nd
• 3. Alberto Leon-Garcia, “Probability and Random Processes for Electrical Engineering”, 2 Edition, Pearson

REFERENCE BOOKS:

• 1. Athanasios Papoulis, S. Unnikrishna Pillai, “Probability, Random Variables and Stochastic Processes”, TMH, 2008
• 2. Henry Stark, John W. Woods, “Probability and Random Processes with Applications to Signal rd Processing”, 3 Edition, Pearson
• 3. Roy D. Yates, David J. Goodman, “Probability and Stochastic Processes – A Friendly Introduction for Electrical and Computer Engineers”, John Wiley & Sons.