# ELEC 471: Random Signals and Noise Bucknell University Spring, 1999

## Overview:

This is an introductory course in probability and statistics for undergraduate and graduate students. Our goal is to study and understand the basic concepts and tools of probability and statistics. We will try provide hands-on experience with the course material through demonstrations and projects using MATLAB. We will also strive to convey the relevance and usefulness of probability and statistics in practical engineering problems.

## Instructor and Office Hours:

Richard J. Kozick
Office: Room 220 Dana
Phone: (570) 577-1129
FAX: (570) 577-1822
Email: kozick@bucknell.edu
Web: http://www.eg.bucknell.edu/~kozick

Office hour schedule for Spring, 1999 is MWF 2 - 3 PM.
I can also meet MWF 12 - 1 PM, but please give me advanced warning for these times by sending email or calling.

## Prerequisites:

MATH 211 (multivariable calculus) and ELEC 320 (Signals and Linear Systems), or equivalent.

## Required Textbook:

Probability and Stochastic Processes: A Friendly Introduction for Electrical & Computer Engineers, Roy D. Yates and David J. Goodman, John Wiley Publishers, 1999.

** PLEASE BRING THE TEXTBOOK TO CLASS **

## Other Books:

Many books are available on the subjects of probability and statistics. The books take many perspectives: some are mathematical, while others are oriented toward engineering, science, business, social science, etc. I can recommend other books with an electrical engineering flavor, if you are interested.

The home page for the ELEC 471 course is located at the URL
http://www.eg.bucknell.edu/~kozick/elec471/elec471.html
http://www.eg.bucknell.edu/~kozick

The course home page contains the homework assignments, syllabus, sample MATLAB programs, and other course information.

```10 quizzes (<= 30 minutes) at 4% each     40%
2 1-hour exams at 10% each                20%
Final exam                                15%
Homework and projects                     15%
Presentations                             10%
```
The grading will be objective, so you will be evaluated with respect to an absolute scale rather than in comparison with your classmates. There are no limits on the number of A's, B's, etc.

## Quizzes and Exams:

We will have two one-hour exams on the following dates:
Exam 1: Thursday, February 4, 1999           Exam 2: Thursday, March 18, 1999

We will also have 10 quizzes during the semester. The only class dates that will not have a quiz are February 4 and March 18 (since we will have exams on those days), and February 11. These quizzes will follow closely with the material from the previous class session and the homework assignments. Missed quizzes cannot be made up, so it is important that you attend all class sessions.

Some quizzes and exams may require you to use MATLAB. The course will conclude with a final exam.

## Homework, Projects, and Presentations:

Homework will be assigned weekly. A subset of the homework problems will be collected and graded. You are responsible to understand all of the homework problems, since the quizzes will be based primarily on the homework assignments and class notes.

There will also be "project" assignments that provide hands-on experience with the course material, often involving processing with MATLAB.

Each student will be asked to prepare a 10-15 minute presentation to the class. The presentations will be done in groups of 2 or 3 students, and I will assign the topic. In many cases, the groups will present their solution to a problem. Your presentation should be well-prepared and clear.

Late homework and project assignments will not be accepted, since we will review the solutions during class. You are encouraged to work on the homework and projects with groups of your classmates. However, the work that you submit for grading must be written individually.

## Course Topics:

Our goal is to study the following topics related to probability and statistics. In the Yates/Goodman text, we will study chapters 1-5 and selected topics from chapters 6, 7, 9, and 10.
• Probability (what it means, axioms)
• Random variables
• Probability mass function (pmf) and probability density function (pdf)
• Cumulative distribution function (cdf)
• Expectation, mean, variance, higher moments
• Conditional probability and conditional expectation
• Joint probability distributions
• Independence and correlation of random variables
• Moment generating function
• Useful probability distributions (Gaussian, uniform, binomial, Poisson, and others)
• Laws of large numbers
• Random processes
• Statistical inference: detection and estimation (least squares, maximum likelihood, Cramer-Rao bound)
• Applications to digital communications and statistical signal processing (matched filter, Wiener filter)
Above is my "wish list" of topics for the ideal course. I am certain that we will not be able to discuss everything on the list. Indeed, the last three topics in the list are typically covered in five to six graduate-level EE courses!