EECS 422: Random Processes in Communications and Control I
Winter 2015


Lecture 1Introduction, Probability spaces, properties of probability measures, conditional probability.
Lecture 2 Statistical independence, Conditional independence, repeated trials, random variables, CDFs, PMFs, PDFs, mixed and singular random variables.
Lecture 3 Multiple random variables, joint distributions, stochastic processes, the Bernoulli process.
Lecture 4Expected Values, Moments, Moment generating functions, sums of random variables, conditional expectation.
Lecture 5Markov's inequality, Chebyshev's inequality, Chernov bounds.
Lecture 6Mean-squared convergence, convergence in probability, almost sure convergence, convergence in distribution, laws of large numbers.
Lecture 7The Central Limit theorem, Poisson Processes.
Lecture 8More on Poisson Processes.
Lecture 9 Markov Chains: transistion matrices/graphs, first-step analysis.
Lecture 10Markov Chains: state classifications, stationary distributions.
Lecture 11Markov Chains: 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 2014 can be found here.