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EECS 401: Probabilistic Methods in Engineering

Instructor: Mingyan Liu, Sandeep Pradhan, Clayton Scott

Coverage
This course covers basic concepts of probability theory and random processes. Subjects include: set theory, axioms of probability, basic principles of counting, conditional probability, independence, discrete and continuous random variables, functions of random variables, probability distribution functions, joint and conditional distribution, expectation, law of large numbers, introduction to discrete and continuous random processes, power spectral density.

Textbook(s)
Required:
1) Dimitri. P. Bertsekas and John. N. Tsitsiklis, Introduction to Probability, 2nd Edition, Athena Scientific, 2008.
Recommended:
1) Roy. D. Yates and David. J. Goodman, Probability and Stochastic Processes, A Friendly Introduction for Electrical and Computer Engineers, 2nd Ed., Wiley.
2) Sheldon Ross, A First Course in Probability, 6th Ed., Prentice Hall.
3) A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd Ed., Addison Wesley.

Syllabus
1) Basic Concepts of Probability: set theory, sample space, axioms of probability, elementary properties, basic principle of counting, joint and conditional probability, Baye's rule, independence.

2) Random Variables and Functions of Random Variables: discrete and continuous random variables, distribution function, density function, common densities, conditional densities and distribution functions, expectation and variance, functions of random variables, expectation, moments, characteristic functions, joint distribution functions, joint probability densities, conditional distribution and density functions, independence, conditional expectation, correlation and covariance.

3) Limit Theorems: inequalities, law of large numbers, central limit theorem.

4) Random Processes: definition of random processes, stationarity and ergodicity, autocorrelation, wide-sense stationarity, Bernoulli, Poisson, Gaussian random processes.

5) Spectral Characteristics of Random Processes: review of linear systems and filtering, power spectral density for deterministic signals, power spectral density for random processes.