Download Probability, Random variable and Stochastic Process

EC601
Probability, Random Variable and Stochastic Process
3-0-0; Credit: 3; Lectures- 42
PREREQUISITE

Basics of sets, set operations, algebra
COURSE OBJECTIVE
 The subject introduces the probability, random & stochastic process that is required for the
theoretical analysis of the communication systems.
COURSE CONTENT
Unit-I: Fundamentals of Probability and Random Processes with applications to networks,
communication, signal processing and control.
Unit-II: Sample space, events and probability law, classical, relative-frequency and axiomatic definitions
of probability.
Unit-III: Conditional probability, independence, total probability, Bayes’ rule; repeated trials.
Unit-IV: Random variables: probability distribution, density and mass functions, functions of a random
variable; expectation, characteristic and moment-generating functions; Chebyshev, Markov and
Chernoff bounds.
Unit-V: Jointly distributed random variables: joint distribution and density functions, joint moments,
conditional distributions and expectations, functions of random variables; random vector- mean vector
and covariance matrix, Gaussian random vectors.
Unit-VI: Random vectors, Law of large numbers, Central limit theorem, Estimation and Detection.
Unit-VII: Stationarity: strict-sense stationary and wide-sense stationary (WSS) processes: time averages
and ergodicity; spectral representation of a real WSS process-power spectral density, cross-power
spectral density, linear time-invariant systems with WSS process as an input- time and frequency
domain analyses
Unit-VIII: Examples of random processes: white noise, Gaussian, Poisson and Markov processes with
applications in communication and signal processing.
TEXT BOOKS
1. Probability, Random variables and Stochastic processes- A. Papoulis & S.U. Pillai, McGraw Hill,
4th Edition, 2001
REFERENCE BOOKS
1. Random Signals – K. Sam Shanmugan & A. M. Breipohi
2. Probability and Random Processes- Miller & Childers, Elsvier, 2004
COURSE OUTCOMES
Students would be able to –
CO1: Solve the problems associated with basic probability
CO2: Solve the problem associated with transformation of random variables
CO3: Summarize the concepts associated with multiple random variables and to solve the problems
associated with Multivariate Gaussian random vector
CO4: Summarize the concepts associated with random process and to compute the power spectral
density of the output of the system.
CO5: Recognize the usage of random process in telecommunication engineering and to solve the
corresponding problems.