ECE 3100 - Introduction to Probability and Inference for Random Signals and Systems

(crosslisted)
(also ENGRD 3100)

Fall, summer. 4 credits.

Prerequisite: MATH 2940, PHYS 2213, or equivalents.

Staff.

Introduction to probabilistic techniques for modeling random phenomena and making estimates, inferences, predictions, and engineering decisions in the presence of chance and uncertainty. Probability measures, classical probability and combinatorics, countable and uncountable sample spaces, random variables, probability mass functions, probability density functions, cumulative distribution functions, important discrete and continuous distributions, functions of random variables including moments, independence and correlation, conditional probability, Total Probability and Bayes’ rule with application to random system response to random signals, characteristic functions and sums of random variables, the multivariate Normal distribution, maximum likelihood and maximum a posteriori estimation, Neyman-Pearson and Bayesian statistical hypothesis testing, Monte Carlo simulation. Applications in communications, networking, circuit design, device modeling, and computer engineering.

Outcome 1: Become fluent in combinatorics and set manipulations so as to make probabilistic predictions
involving discrete models.

Outcome 2: Learn to recognize random phenomena in ECE applications, select appropriate mathematical
models for them, and solve those models by exploiting mathematical structure such as statistical independence.

Outcome 3: Understand the statements of key limit theorems and be able to apply those theorems to make
decisions in the presence of uncertainty.

Outcome 4: Formulate estimation and detection problems from described physical scenarios and compute
the optimal estimators/decision rules for those scenarios.