EECS 495 - Probabilistic Systems and Random Signals
CATALOG DESCRIPTION: Basic concepts of probability theory and statistics, random variables, moments; multiple random variables, conditional distributions, correlation; random signals; applications to engineering systems. NOTE: This is the graduate level version of EECS 302; additional material and different homework will be provided for EECS 495.
REQUIRED TEXTS: A. Haddad, Probabilistic Systems and Random Signals , Prentice Hall, 1 st edition
REFERENCE TEXTS: None
COURSE COORDINATOR: Abraham Haddad
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.
PREREQUISITE: Mathematics 234
DETAILED COURSE TOPICS
Week 1: Techniques for Summarizing and Simulating Data, Sample Space.
How data is represented, models for random experiments, sample space, basic definition of probability.
Week 2: Basic Probability Concepts - Conditional Probability, Bayes' Rule.
Conditional probability and independence, Bayes' rule, applications to error models and reliability.
Week 3: Random Variables - Models of Random Variables and Distributions.
Distributions, discrete and continuous, basic engineering examples.
Week 4: Averages, Functions, and Various Important Distributions.
Averages, functions of random variables, conditional distributions, applications to signals, systems and networks.
Week 5: Joint Random Variables, Independence .
Joint densities and distributions, basic discrete and continuous examples, independent random variables.
Week 6: Functions of Random Variables, Correlation.
Sum of two random variables, functions of two random variables, averages and correlation, applications to the processing of signals.
Week 7: Gaussian Random Variables.
Joint Gaussian Random variables, applications to signals and noise, Rayleigh distribution, envelope of sinusoidal signals.
Week 8: Multiple Random Variables, Central Limit Theorem, Simulation.
Independent multiple random variables, sums of random variables, law of large numbers, central limit theorem, Monte Carlo simulation, applications to signals and systems.
Week 9: Basic statistics and applications in engineering.
Data analysis; sample mean and sample variance; histograms; convergence of sample mean.
Week 10: Introduction to Random Processes.
Basic definitions of discrete-time and continuous time random signals, sample paths, autocorrelation function, second-order properties, applications to signals and noise.
COMPUTER USAGE: Matlab Assignments
LABORATORY PROJECTS: None
- Homework - 20%
- Matlab Assignments - 10%
- Midterm - 30%
- Final - 40%
COURSE OBJECTIVES: When a student completes this course, s/he should be able to:
• Understand the basic concepts of probability and how they arise in engineering systems.
• Analyze systems involving uncertainties using random variable models.
• Understand the concepts of distributions, correlation, and other averaging properties.
• Design systems for extracting useful information from noisy data.
• Design simple reliable engineering systems in the presence of errors and failures.
• Understand the basic elements of statistics and analysis of data.
ABET CONTENT CATEGORY: 50% Math and Basic Science, 50% Engineering.