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Courses Detail Information

ECE6601J – Probability and Random Processes

Instructors:

Credits: 3 credits

Pre-requisites: ECE4010J

Description:

The goal of this course it to learn how to work with probabilistic models of random experiments, as needed for
subsequent graduate courses and research. The course covers several ways of describing such experiments
(probability models, random variables, random vectors, and random processes) and several ways of describing their
probability distribution (probability measures: distribution, mass and density functions). Much of the course is
concerned with how to compute various probabilistic quantities (e.g. event probabilities, expected values, correlations,
best estimates, frequency spectra) from other probabilistic quantities (e.g. density functions). The course topics are
similar to those covered in Ve401, but a deeper level of understanding is expected, more attention is paid to
mathematical formulation, and there is more coverage of random processes.

Course Topics:

Models of random experiments
Axioms and properties of probability
Conditional probability
Independence of events
Combinatorics and probability
Introduction to Random Variables
PMF and Discrete Random Variables
PDF and Continuous Random Variables
Gaussian CDF
Conditional Probability
Function of a RV
Expectation of a RV
Transform Methods and Probability Generating Function
Two Random Variables
Marginal PDF
Functions of Two Random Variables
Conditional PDF
Joint Moments
Mean Square Error Estimation
Markov and Chebyshev Inequalities
Random Vectors
Sample Mean
Convergence of Random Sequences
Central Limit Theorem
Introduction to Random Processes
Brownian Motion
Poisson Process
Complex RV and RP
Stationarity
PSD, QAM, White Noise
Response of Systems
LTI Systems and RPs
Response of Systems
LTI Systems and RPs
Computing State Probabilities
Continuous-time MC
Ergodicity Theorems
Series Expansions