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

Spring. 4 credits. Letter grades only.

Prerequisite: MATH 2940 and PHYS 2213, or equivalent.

Q. Zhao.

Probability theory is a mathematical discipline that allows one to reason about uncertainty: it helps us to predict uncertain events, to make better decisions under uncertainty, and to design and build systems that must operate in uncertain environments. This course will serve as an introduction to the subject on the modeling and analysis of random phenomena and processes, including the basics of statistical inference in the presence of uncertainty. Topics include probability models, combinatorics, countable and uncountable sample spaces, discrete random variables, probability mass functions, continuous random variables, probability density functions, cumulative distribution functions, expectation and variance, independence and correlation, conditioning and Bayess rule, concentration inequalities, the multivariate Normal distribution, limit theorems (including the law of large numbers and the central limit theorem), Monte Carlo methods, random processes, and the basics of statistical inference. Applications to communications, networking, circuit design, computer engineering, finance, and voting will be discussed throughout the semester.

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.