Course Details
Subject {L-T-P / C} : EC3503 : Probability and Random Variables { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Siddharth Deshmukh
Syllabus
Introduction to probability: Sample space, outcomes and events. Axioms and properties of probability. Random variables: Conditions for function to be random variable. Discrete and continuous random variable. Distribution function. Density function. Binomial, Poisson, Uniform, Exponential, Gaussian, Rayleigh density functions. Conditional distribution and density functions. The central limit theorem. Reliability. Operations on random variables: Expectation. Week and strong law of large numbers. Conditional expectation. Expectation of function of random variable. Moments about origin and central moments. Variance, skew and kurtosis. Chebychev’s and Markov inequalities. Characteristic function. Moment generating function. Chernoff’s inequality and bounds. Transformation of discrete and continuous random variables. Multiple Random Variables: Vector of random variables. Joint distribution. Marginal distribution. Conditional distribution and density: Point and interval conditioning. Statistical independence. Distribution and density of sum and product of random variables. Gaussian Random variables: Bivariate, Multivariate Gaussian. Joint characteristic, density function. Linear transformation of Gaussian random variables. Complex Gaussian random variables. Random Processes: Definition and characteristic of random processes. Strict-sense and wide-sense random processes. WSS through LTI systems. Power spectral density of WSS processes. Characterization of correlation function. Matched filter. Wiener filter. Wiener-Khinchin theorem. Ergodic process. Introduction to Poisson process, Renewal and Wiener and Markov process.
Course Objectives
- To introduce concepts on about random variables and random process
- To build capability to statistically characterize and model physical systems
- To build capability to solve problems related to random variables and random processes
Course Outcomes
1. Students will have understanding about random variables and random process. <br />2. Students will be able to statistically characterize and mode physical systems. <br />3. Students will be able to solve problems related to random variables and random processes.
Essential Reading
- Peyton Z Peebles Jr., Probability, Random Variables, and Random Signal principles, McGraw Hill , 4th Edition 2002
- Athanasios Papoulis, Probability, Random Variables and Stochastic Processes, McGraw Hill , 4th Edition 2002
Supplementary Reading
- John A. Gubner, Probability and Random Processes for electrical and Computer Engineers, Cambridge , 1st Edition 2006
- R G Gallager, Stochastic Processes: Theory for Applications, Cambridge University Press , 1st Edition 2013