EECS 422: Random Processes in Communications and Control I
Winter 2010

Lectures from 2010

Lecture 1Introduction, Probability spaces.
Lecture 2Properties of probability measures, conditional probabilities, independence.
Lecture 3 Independent trials, combinations, permutations.
Lecture 4 Random variables, distributions, discrete Random variables, p.m.f.'s
Lecture 5 Continuous random variables, densities, mixed random variables, examples of common distributions.
Lecture 6Gaussian random variables, conditional distributions, functions of random variables.
Lecture 7 Expected values, moments.
Lecture 8 Markov inequality, Chebyshev's inequality, Chernoff bounds, moment generating functions, Characteristic functions.
Lecture 9Introduction to random vectors, joint distributions, joint densities, marginals.
Lecture 10More on Random vectors: independence, moments, correlation.
Lecture 11Two jointly Gaussian random variables, functions of random vectors.
Lecture 12Linear transformations of random vectors, condition distributions.
Lecture 13More on conditional distributions, conditional expectation, MMSE estimation.
Lecture 14More on MMSE estimation; scalar Gaussian case.
Lecture 15MMSE estimation - vector case; jointly Gaussian Random variables (N>2).
Lecture 16More on Jointly Gaussian random variables and MMSE estimation; covariance matrices.
Lecture 17Laws of large numbers, mean-square convergence, convergence in probability.
Lecture 18Almost sure convergence; strong law of large numbers; convergence in distribution; the central limit theorem.
Lecture 19More on the central limit theorem; random processes.
Lecture 20Discrete-time Random processes: Bernoulli processes, Binomial counting process, simple random walk; stationarity, Memoryless and Markov properties, independent and stationary increments.
Lecture 21Random walk on a graph; Poisson processes.
Lecture 22More on Poisson processes; random telegraph signals.
Lecture 23Formally specifying random processes, Kolmorogorov's consistency conditions; mean and correlation/covariance functions; wide sense stationarity.
Lecture 24Properties of covariance functions; Brownian motion.
Lecture 25Mean-squared continuity, mean-squared derivatives.
Lecture 26Mean-squared integration; random processes and linear systems.
Lecture 27Spectral analysis for random processes; application to linear systems.
Lecture 28Introduction to optimal filtering; overview of related courses.