Course Description
This is a graduatelevel course that teaches basics of random process theory with applications to communication theory and systems. Important topics include analysis of common random processes (e.g. Poisson process, White Noise, Wiener Process, etc.), random sequences, random processes in linear systems, Markov chains, meansquare calculus.
The textbook used for the course is, "Probability, Statistics, and Random Processes for Engineers+, 4th Edition, by H. Stark and J. W. Woods.
The comprehensive set of videos listed below now cover all the topics in the course; 116 videos with nearly 21 hours of content.
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Video Lectures

Random Vectors: (14 videos, ~164 minutes)

Topics include: density and distribution functions, uncorrelated vectors, orthogonal vectors, transformations of random vectors, covariance matrices, eigenvalues/eigenvectors of covariance matrices, covariance diagonalization, Gaussian random vectors.


Random Sequences

Part 1: (17 videos, ~202 minutes)

Topics include: random sequence definition, mean function autocorrelation function, Bernoulli random sequence, arrival time random sequence, random walks, random sequences in discretetime linear systems


Part 2: (11 videos, ~78 minutes)

Topics include: Widesense stationary (WSS) random sequences, autocorrelation function properties, simplified input/output relationships for WSS random sequences in linear systems, the power spectral density (PSD) function, PSD properties, and PSD examples in Matlab.


Part 3: (9 videos, ~117 minutes)

Topics include: Markov random sequences, Markov chains, state transition matrices, probability row vectors, convergence of sequences, sure convergence, almost sure convergence, and meansquare convergence.



Random Processes

Part 1: (10 videos, ~86 minutes)

Topics include: Random process definition, mean and autocorrelation functions, asynchronous binary signaling, Poisson random process and properties


Part 1 Cont: (6 videos, ~73 minutes)

Topics include: Telegraph random process, PSK random process, Wiener random process (i.e. random walk random process) and properties


Part 2: (10 videos, ~106 minutes)

Topics include: Markov random processes, Markov chains, statetransition diagrams, random processes in continuoustime linear systems, input/output relationships for mean and autocorrelation functions, white noise random processes


Part 3: (8 videos, ~77 minutes)

Topics include: Random process properties, simplified input/output relationships for WSS random processes, the power spectral density (PSD) function, PSD properties, and PSD examples.


Part 4: Additional Classification (4 videos, ~35 minutes)

Topics include: Widesense periodic random processes, cyclostationary random processes, and PSK power spectral density



Mean Square (MS) Calculus

Part 1: (13 videos, ~120 minutes)

Topics include: Meansquare calculus introduction, meansquare continuous definition and examples, meansquare derivative definition and examples, meansquare integral definition and examples


Part 2: (6 videos, ~135 minutes)

Topics include: Definitions of mean ergodic, meansquare ergodic, and correlation ergodic random processes; KarhunenLoeve expansion definition, examples (with Matlab), and proofs.


Example Problems

Random Vectors (5 videos, ~36 minutes)
Practice Problems
File Downloads