Probability and Random Processes detailed syllabus scheme for B.Tech Electronics & Telecommunication Engineering (ET), 2017 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 all other DBATU Syllabus for Electronics & Telecommunication Engineering 5th Sem 2017, do visit ET 5th Sem 2017 Onwards Scheme. The detailed syllabus scheme for probability and random processes is as follows.
Probability and Random Processes Syllabus for Electronics & Telecommunication Engineering (ET) 3rd Year 5th Sem 2017 DBATU
Course Objectives:
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Course Outcomes:
On successful completion of the course, students should be able to:
- Explain fundamentals of probability theory, random variables and random processes.
- Understand the mathematical concepts related to probability theory and random processes.
- Understand the characterization of random processes and their properties.
- Formulate and solve the engineering problems involving random processes.
- Analyze the given probabilistic model of the problem.
- Make precise statements about random processes.
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
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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 independence, 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
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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, Linear time-invariant system with a WSS process as an input: sationarity of the output, autocorrelation 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, Spectral factorization theorem, Examples of random processes: white noise process and white noise sequence; Gaussian process; Poisson process, Markov Process.
Reference/Text Book:
- Probability and Random Processes by Geoffrey Grimmett, David Stirzaker
- Probability, random processes, and estimation theory for engineers by Henry Stark, John William Woods.
For detail syllabus of all other subjects of Electronics & Telecommunication Engineering (ET) 5th Sem 2017 regulation, visit ET 5th Sem Subjects syllabus for 2017 regulation.