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# 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

3

### Learning 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.

20 / 80

### Homework:

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.

No Projects

### Exams:

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.

### Computer Requirements:

ProEd minimum computer requirements; Internet access required to download the homework from the course web pages.

None.

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