# ECE 30200 - Probabilistic Methods in Electrical and Computer Engineering

## Course Details

Lecture Hours: 3 Credits: 3

• CMPE Core
• EE Core

### Normally Offered:

Each Fall, Spring, Summer

### Requisites:

(MA 26200 or MA 26600 or MA 36600) and ECE 30100 [may be taken concurrently].

### Catalog Description:

An introductory treatment including probability of events, discrete and continuous random variables, multiple random variables, sums of random variables and long-term averages, and elementary random processes. Applications involving uniform, Gaussian, exponential, geometric and related random variables. Introduction to parameter estimation and hypothesis testing. Discussion of wide-sense stationary random processes, including correlation functions, spectral densities and the response of linear time invariant systems. Course examples are drawn from signal processing, wireless communications, system reliability, and data science.

### Course Objectives:

This course is intended to introduce the concepts of probability and random processes and to discuss their application to engineering problems. Particular emphasis is given to application of these methods to systems analysis. It is also intended that this course should be a suitable prerequisite for EE 60000.

### Required Text(s):

1. Probability, Statistics, and Random Processes for Electrical Engineering , 3rd Edition , Alberto Leon-Garcia , Prentice-Hall , 2008 , ISBN No. 9780131471221

### Recommended Text(s):

1. MatLab: Student Version , Current Edition , The MathWorks, Inc.

### Learning Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:
1. an ability to solve elementary probability problems involving random events and random variables. 
2. an ability to model uncertainty by random variables and analyze the implications in a range of engineering applications. [1,6]
3. an understanding of the idea of a random process, along with some basic examples and applications. [1,6]

### Lecture Outline:

Lectures Topic
6 Introduction, set theory, probability axioms, conditional probability, Bayes rule, total probability, independence, Bernoulli trials
10 Random variables and mass, density and distribution functions; function of a random variable; mean, variance and moments; conditional cdf, pdf and pmf given an event; total cdf, pdf, pmf, expectation and variance
4 Gaussian, uniform, exponential, geometric, and related random variables; properties and applications
10 Multiple random variables and joint and conditional mass, density and distribution functions; independence, correlation, and covariance; functions of random variables; jointly Gaussian random variables
6 Sums of random variables and long-term averages; estimation of mean and variance; introduction to signal detection and estimation
6 Random processes, interpretations and examples; wide-sense stationary random processes, correlation functions and spectral densities; response of linear time-invariant system to wide-sense stationary inputs and applications
3 Tests

none