WUSTL ESE 520 - SyllabusESE520Fall14 (2 pages)

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SyllabusESE520Fall14



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SyllabusESE520Fall14

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Pages:
2
School:
Washington University in St. Louis
Course:
Ese 520 - Probability and Stochastic Processes
Probability and Stochastic Processes Documents

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SYLLABUS The chapter and section references refer to the text Probability and Random Processes for Electrical and Computer Engineers by John A Gubner 1 Introduction Probability Spaces what do we mean by the word probability probability spaces finite countable and uncountable models sections 1 1 1 3 elementary probability theory sections 1 4 1 7 conditional probability and Bayes s theorem sections 1 5 1 6 2 Random Variables and Distribution discrete and continuous random variables sections 2 1 2 3 4 1 5 1 5 3 Examples binomial Poisson exponential Gaussian sections 3 2 4 1 functions of random variables section 5 4 joint and marginal distributions sections 7 1 7 2 n dimensional Gaussian distributions sections 7 4 7 5 9 1 9 2 3 Expectation mean variance and covariance sections 2 4 4 4 independence and conditional distributions sections 3 4 7 3 conditional expectation a naive discussion sections 3 5 7 3 least squares estimation for Gaussian random vectors sections 9 4 9 5 characteristic functions sections 3 1 4 3 9 3 1 4 Limit theorems laws of large numbers sections 3 3 central limit theorem section 5 6 5 Stochastic Processes Foundations finite dimensional distributions and a discussion of Kolmogorov s theorem on the existence of stochastic processes sections 10 110 2 11 4 existence of continuous versions quote only 6 Poisson process section 11 1 axiomatic definition characterization as counting process with stationary and independent increments inter arrival times 7 Gaussian processes with Wiener process as example covariance function and spectral density sections 10 3 10 4 Wiener process Brownian motion section 11 3 equivalent characterizations and elementary properties white noise a naive introduction sections 10 5 10 6 8 An Brief Introduction to Markov processes Chapman Kolmogorov equations Homogeneous Markov chains sections 12 1 12 4 only if time permits 2



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