COURSE TITLE: EECS 302 Probabilistic Systems and Random Signals

CATALOG DESCRIPTION (2008-09): Basic concepts of probability theory and statistics, random variables, moments; multiple random variables, conditional distributions, correlation; random signals; applications to engineering systems.

REQUIRED TEXTS: A. H. Haddad, *Probabilistic Systems and Randopm Signals, *
Prentice-Hall, 2006

COURSE GOALS: To teach students the basic concepts of probability theory and statistics, random variables, conditional distributions, and correlation as they arise in engineering signal and systems models.

PREREQUISITES: Mathematics 215

DETAILED COURSE TOPICS

** * Week 1 (Sept. 24, 2013)**: Techniques for Summarizing and Simulating Data, Sample Space.
Ch. 1.1 to 2.3

How data is represented, models for random experiments, sample space, basic definition of probability.

** *Week 2 (Sept. 30, 2013)**: Basic Probability Concepts - Conditional Probability, Bayes' Rule.
Ch. 2.3 to 2.7

Conditional probability and independence, Bayes' rule, applications to error models and reliability.

** *Week 3 (Oct. 7, 2013)**: Random Variables - Models of Random Variables and Distributions.
Ch. 3.1 to 3.3

Distributions, discrete and continuous, basic engineering examples.

** *Week 4 (Oct. 14, 2014)**: Averages, Functions, and Various Important Distributions.
Ch. 3.3 to 4.3

Averages, functions of random variables, conditional distributions, applications to signals, systems and networks.

*** Weeks 5 (Oct. 21, 2013)**: Joint Random Variables, Independence. Ch. 5.1 to 5.4

Joint densities and distributions, basic discrete and continuous examples, independent random variables

** * Weeks 6 (Oct. 28, 2013)**: Conditional distributions and densities. Ch. 5.5 to 6.1

Conditional densities.

Midterm and midterm review

** *Week 7 (Nov. 4, 2013)**: Functions of Random Variables, Correlation. Ch. 6.2 to 6.5

Sum of two random variables, functions of two random variables, averages and correlation, applications to the processing of signals

Joint Gaussian Random variables, applications to signals and noise, Rayleigh distribution, envelope of sinusoidal signals.

** *Week 8 (Nov. 11, 2013)**: Multiple Random Variables, Central Limit Theorem, Simulation. Ch. 8

Independent multiple random variables, sums of random variables, law of large numbers, central limit theorem, Monte Carlo simulation, applications to signals and systems

Start Statistics. ** *Weeks 9 (Nov. 18, 2013)**: Basic Statistics and Reliability. Ch. 9 and 11

Data analysis; sample mean and sample variance; histograms; convergence of sample mean.

Introduction to reliability: series, parallel and stand-by connections

** *Weeks 10 & 11 (Nov. 25, 2013 to Dec. 6, 2013)**:

Introduction to random processes: Discrete-time case. Continuous-Time Random Processes. Ch. 12 and 13

Basic definitions, sample paths, auto-correlation function, second-order properties, applications to signals and noise

COMPUTER USAGE: Matlab Assignments

LABORATORY PROJECTS: None

GRADES:

* Homework (including Matlab)- 30%

* Midterm - 35%

* Final - 35%

COURSE OBJECTIVES: When a student completes this course, s/he should be able to:

1. Understand the basic concepts of probability and how they arise in engineering systems

2. Analyze systems involving uncertainties using random variable models

3. Understand the concepts of distributions, correlation, and other averaging properties

4. Design systems for the extracting useful information from noisy data

5. Design simple reliable engineering systems in the presence of errors and failures

6. Understand the basic elements of statistics and analysis of data