Random Variables and Signals
Engineering applications of probability theory; problems on events, independence, random variables, probability distribution and density functions, expectations, and characteristic functions; dependence, correlation, and regression multivariate Gaussian distribution; stochastic processes, stationarity, ergodicity, correlation functions, spectral densities, random inputs to linear systems; Gaussian processes.
ECE60000
Credit Hours:
3Learning Objective:
To introduce the topics of probability, random variables, and stochastic processes at the graduate level.Description:
Engineering applications of probability theory; problems on events, independence, random variables, probability distribution and density functions, expectations, and characteristic functions; dependence, correlation, and regression multivariate Gaussian distribution; stochastic processes, stationarity, ergodicity, correlation functions, spectral densities, random inputs to linear systems; Gaussian processes.
Topics Covered:
Engineering applications of probability theory; problems on events, independence, random variables, probability distribution and density functions, expectations, and characteristic functions; dependence, correlation, and regression multivariate Gaussian distribution; stochastic processes, stationarity, ergodicity, correlation functions, spectral densities, random inputs to linear systems; Gaussian processes.Prerequisites:
Graduate standing; knowledge of basic set theory, matrix analysis, continuous and discrete time signal and systems analysis, Fourier transforms.Applied / Theory:
20 / 80Homework:
Homework will be assigned each week, but will not be collected or graded; the homework and solutions will be available on the course web site.Projects:
No ProjectsExams:
Three exams and one final exam.Textbooks:
Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.Tentative: Required--A. Papoulis, "Probability, Random Variables, and Stochastic Processes," 4th ed., McGraw-Hill Europe. ISBN 9780071226615.