# ECE 3077 Summer 2014

Instructor
Justin Romberg
Email: jrom@ece.gatech.edu
Office: Centergy 5227
Phone: 404-894-3930

Description
ECE 3077 is a a foundational course in probability.  The central theme of the course is the development of mathematical methods for understanding and modeling uncertainty.

### Outline

I. Introduction to probability
(a) simple probability models, the Kolmogorov axioms, the uniform law
(b) independence
(c) conditional probability and Bayes rule
(d) basic combinatorics and counting

II. Discrete random variables
(a) probability mass functions (pmfs)
(b) expectation, variance, and moments
(c) multiple discrete random variables, joint pmfs
(d) conditional pmfs
(e) example distributions: Bernoulli, Binomial, Geometric, Poisson, etc.

III. Continuous random variables
(a) probability distributions and probability density functions (pdfs)
(b) multiple continuous random variables, joint pdfs
(c) conditional pdfs
(d) example distributions: Uniform, Exponential, Gaussian/Normal, etc.

IV. Functions of random variables
(a) derived distributions
(b) generating arbitrary random variables from a uniform random variable
(c) adding independent random variables (d) central limit theorem

V. Basic statistics
(a) sample mean and variance
(b) confidence intervals, the student-t distribution
(c) parameter estimation using maximum likelihood (d) parameter estimation using Bayesian inference