EECS 422: Random Processes in Communications and Control I
Winter 2018


Lecture 1Introduction, Probability spaces, Sigma Algebras, Properties of probability measures, Sect. 1.1-1.2
Lecture 2 Conditional probability, Statistical independence, conditional independence, Repeated trials, random variables, CDFs, PMFs, PDFs, mixed and singular random variables. Sect. 1.3.1-1.3.3
Lecture 3 Multiple random variables, joint distributions, stochastic processes, the Bernoulli process.Sect. 1.3.4 -1.4
Lecture 4 Expected values, moments, sums of random variables, conditional expectation, The coupon collector problem.Sect. 1.5
Lecture 5Markov's inequality, Chebyshev's inequality, Chernov Bounds. Sect. 1.6
Lecture 6 Moment generating functions and sums of independent random variables, log-moment generating functions, Convergence of random variables: mean-squared convergence, convergence in probability, the weak law of large numbers.Sect. 1.6-1.7
Lecture 7Almost sure convergence, the strong law of large numbers, convergence in distribution,, the central limit theorem.Sect. 1.7 & 5.2
Lecture 8 Central limit theorem examples, Characteristic functions, Counting Processes and the Poisson Process, memoryless property, fresh-restart property.Sect. 2.1-2.2
Lecture 9 More on Poisson Processes: increment properties, alternative definitions, Splitting and combining Poisson Processes. Sect. 2.2-2.3
Lecture 10Markov Chains: definitions, transition Matrices/Graphs, first-step analysis.Notes
Lecture 11 MID-TERM EXAM
Lecture 12Markov Chains: Stationary distributions, state classifications, recurrence, periodicity. Sect. 4.1-4.2 & 6.2
Lecture 13Markov Chains: ergodic chains, convergence to stationary distributions, balance equations.Sect. 4.2-4.3, 6.1-6.2
Lecture 14Gaussian random vectors: linear transformations, moment generating functions.Sect. 3.1 -3.3
Lecture 15Gaussian random vectors: joint probability distributions and properties of covariance matricesSect. 3.3 -3.4
Lecture 16 Conditioning and Gaussian random vectors; Introduction to estimationSect. 3.5, Sect. 10.1.
Lecture 17 Estimation and Gaussian random vectors, linear estimation, Intro. to Gaussian Processes. Sect. 10.2-10.3.
Lecture 18Stationary processes, Properties of covariance functions, Wiener processes.Sect. 3.6.1, 3.6.9
Lecture 19 More on Wiener prcess, random processes and linear systems, spectral density.

A list of lecture topics from 2017 can be found here.