Probability Theory and Random Processes detailed syllabus scheme for Electronics Engineering (EL), 2019-20 onwards has been taken from the DBATU official website and presented for the Bachelor of Technology students. For Subject Code, Course Title, Lecutres, Tutorials, Practice, Credits, and other information, do visit full semester subjects post given below.
For 5th Sem Scheme of Electronics Engineering (EL), 2019-20 Onwards, do visit EL 5th Sem Scheme, 2019-20 Onwards. For the Elective-I scheme of 5th Sem 2019-20 onwards, refer to EL 5th Sem Elective-I Scheme 2019-20 Onwards. The detail syllabus for probability theory and random processes is as follows.
Probability Theory and Random Processes Syllabus for Electronics Engineering (EL) 3rd Year 5th Sem 2019-20 DBATU
Course Objectives:
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Course Outcomes:
At the end of this course students will demonstrate the ability to
- Understand representation of random signals
- Investigate characteristics of random processes
- Make use of theorems related to random signals
- To understand propagation of random signals in LTI systems.
UNIT – 1 Introduction to Probability
Definitions, scope and history; limitation of classical and relative- frequency- based definitions, Sets, fields, sample space and events; axiomatic definition of probability, Combinatorics: Probability on finite sample spaces, Joint and conditional probabilities, independence, total probability; Bayes’ rule and applications.
UNIT – 2 Random variables
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UNIT – 3 Random vector and distributions
Mean vector, covariance matrix and properties, Some special distributions: Uniform, Gaussian and Rayleigh distributions; Binomial, and Poisson distributions; Multivariate Gaussian distribution, Vector- space representation of random variables, linear indepe ndence, inner product, Schwarz Inequality, Elements of estimation theory: linear minimum mean – square error and orthogonality principle in estimation; Moment – generating and characteristic functions and their applications, Bounds and approximations: Chebysev inequality and Chernoff Bound.
Unit – 4 Sequence of random variables and convergence
Almost sure convergence and strong law of large numbers; convergence in mean square sense with examples from parameter estimation; convergence in probability with examples; convergence in distribution, Central limit theorem and its significance.
UNIT – 5 Random process
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UNIT – 6 Spectral representation of a real WSS process
Power spectral density, properties of power spectral density, cross- power spectral density and properties; auto- correlation function and power spectral density of a WSS random sequence, Line ar time – invariant system with a WSS process as an input: sationarity of the output, auto -correlation and power – spectral density of the output; examples with white -noise as input; linear shift – invariant discrete- time system with a WSS sequence as input, Spe ctral factorization theorem, Examples of random processes: white noise process and white noise sequence; Gaussian process; Poisson process, Markov Process.
Reference Books:
- T. Veerrajan, Probability, Statistics and Random Processes, Third Edition, McGraw Hill.
- Probability and Random Processes by Geoffrey Grimmett, David Stirzaker
- Probability, random processes, and estimation theory for engineers by Henry Stark, John William Woods.
- H. Stark and J. Woods, Probability and Random Processes with Applications to Signal Processing, Third Edition, Pearson Education
- A. Papoulis and S. Unnikrishnan Pillai, Probability, Random Variables and Stochastic Processes, Fourth Edition, McGraw Hill.
- K. L. Chung, Introduction to Probability Theory with Stochastic Processes, Springer International
- P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability, UBS Publishers.
- P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Stochastic Processes, UBS Publishers
- S. Ross, Introduction to Stochastic Models, Harcourt Asia, Academic Press.
For detail syllabus of all subjects of Electronics Engineering (EL) 5th Sem 2019-20 onwards, visit EL 5th Sem Subjects of 2019-20 Onwards.