EECS 422: Random Processes in Communications and Control I
Winter 2016


Lecture 1Introduction, Probability spaces, properties of probability measures, conditional probability, statistical independence, conditional independence.
Lecture 2 Repeated trials, random variables, CDFs, PMFs, PDFs, mixed and singular random variables, Multiple random variables, joint distributions, stochastic processes.
Lecture 3 The Bernoulli process, expected values, moments, sums of random variables, conditional expectation.
Lecture 4The coupon collector problem, Markov's inequality, Chebyshev's inequality, Chernov Bounds, moment generating functions.
Lecture 5Chernov bound examples, Moment generating funcitons and sums of independent random variables, log-moment generating functions.
Lecture 6Convergence of random variables: mean-squared convergence, convergence in probability, almost sure convergence, laws of large numbers.
Lecture 7The strong law of large numbers, convergence in distribution, characteristic functions, the central limit theorem.
Lecture 8Counting Processes and the Poisson Process.
Lecture 9 Splitting and combining Poisson Processes, Markov Property, Markov Chains: transistion matrices/graphs.
Lecture 10Markov Chains: first-step analysis, state classifications, stationary distributions.
Lecture 11Markov Chains: Stationary distributions, Balance equations; Introduction to Gaussian Random Vectors.
Lecture 12 More on Gaussian random vectors.
Lecture 13 Conditioning and Gaussian random vectors; introduction to Gaussian Processes.
Lecture 14Stationary processes, Properties of covariance functions, Weiner processes.
Lecture 15 Orthonormal expansions, Gaussian sinc processes, filtered Gaussian sinc processes.
Lecture 16 Second-order characterizations of filtered random processes, Spectral densities; introduction to estimation.
Lecture 17 MMSE estimation, estimation and Gaussian random vectors, LLSE estimation, optimal filtering.

A list of lecture topics from 2015 can be found here.