EECS 422: Random Processes in Communications and Control I
Winter 2011


Lecture 1Introduction, Probability spaces, properties of probability measures, conditional probability, independence.
Lecture 2Bayes' rule and inference, independent trials, discrete random variables and probability mass functions, cumulative distribution functions, continuous random variables and densities.
Lecture 3Mixed and Singular Random Variables, properties of density functions, Conditional Distributions, functions of random variables, expected values and moments.
Lecture 4Gaussian Random Variables, Markov's Inequality, Chebyshev's Inequality, Chernoff Bounds, Moment Generating Functions.y
Lecture 5 Characteristic Functions; random vectors, joint cdfs, pdfs and pmfs, marginal distributions.
Lecture 6Independence of random variables, Functions of multiple random variables, linear transformations of random vectors, Expectation and moments of random vectors, correlation and covariance.
Lecture 7Linear estimation; Jointly Gaussian pairs of random variables and their properties.
Lecture 8Conditional probability distributions, Conditional expectation, iterated expectations.
Lecture 9Baysian MMSE estimation, estimation and jointly Gaussian random variables.
Lecture 10 Jointly Gaussian random vectors, Covariance matrices, MMSE estimation for random vectors.
Lecture 11 Mean-square convergence, convergence in probability, convergence almost surely, Weak and Strong Laws of Large numbers
Lecture 12 Convergence in distribution, the central limit theorem; introduction to stochastic processes.
Lecture 13 Finite dimensional distributions and Kolmogorov's theorem, Stationary processes, memoryless processes, stationary increments, independent increments, Markov property, counting processes, random walks.
Lecture 14Markov chains, transition matrices/graphs, n-step transistions, first-step analysis, stationary distributions.
Lecture 15Arrival processes/counting processes, Poisson processes.
Lecture 16 Mean and correlation/covariance functions, wide sense stationary processes, Gaussian Processes, Wiener processes.
Lecture 17 Multiple random processes, cross correlation functions, Mean-square calculus.
Lecture 18 Mean-square integration, random processes and linear systems, power spectral density functions.
Lecture 19 Systems driven by white noise; optimal linear filtering; the non-causal Wiener filter; overview of related courses.

A list of lecture topics from 2010 can be found here.