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EECS 401: Probabilistic Methods in Engineering 

Instructor: Mingyan Liu, Sandeep Pradhan, Clayton Scott Coverage Textbook(s) Syllabus 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, widesense 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. 
