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ELECTRICAL, COMPUTER, AND SYSTEMS ENGINEERING DEPARTMENT





ABET COURSE SYLLABUS




ECSE-4500: Probability for Engineering Applications




Course Catalog Description:
Axioms of probability, joint and conditional probability, random variables, probability density and distribution functions, functions of random variables, statistical averages, empirical distributions, parameter estimation, regression, test of hypotheses, and Markov chains. Applications to engineering data such as device characteristics, failure rates, image processing and network traffic. Prerequisites: ECSE-2410; Fall, spring, and summer terms annually. 4 credit hours.







Pre-Requisite Courses:

ECSE-2410







Co-Requisite Courses:

None







Prerequisites by Topic:

  1. Advanced Calculus

  2. Properties of continuous and discrete-time signals
  3. Fourier series and transforms


  4. Time- and frequency-domain linear systems analysis






Textbook:


(and/or other required material)

H. Stark and J. W. Woods, Probability and Random Processes with Applications in Signal Processing, 3rd Edition, Prentice-Hall/Pearson, 2003.







References:

A. Leon-Garcia, Probability, Statistics, and Random Processes for Electrical Engineering, 3rd Ed., Pearson/Prentice-Hall, 2008. A. Papoulis and S. U. Pillai, Probability, Random Variables, and Stochastic Processes, 4th Ed., McGraw-Hill, 2002.






Course Coordinator:

John W. Woods







Overall Educational Objective:

The overall objective of this course is to introduce students to the fundamentals of probability theory and its applications to engineering systems.







Course Objectives:

  1. Understand basic probability.
  2. Be able to apply concepts of probability to model typical computer and electrical engineering problems.


  3. Understand basic statistical methods.

  4. Evaluate the performance of engineering systems with uncertainty.







How Course Objectives

are Assessed:


This course is delivered in lecture format and there is also a recitation session. Homework assignments are assigned on a weekly basis. The course grade will be determined as follows: 2 Tests (10 points each), 2 Exams (25 points each), Final Exam (30 points), and homework (20 points). Total: 120 points.. Students are encouraged to work together on homework assignments.







Relation to EE/CSE/EPE Outcomes

Outcome

Level

Demonstrate Proficiency








N, M, H

e.g. Exams, projects, HW




Mathematics, science and engineering

H

Tests, Exams, HW

N = none

Basic disciplines in Electrical Engineering

N




M = moderate

Depth in Electrical Engineering

M

Tests, Exams, HW


H = high

Basic disciplines in Computer & Sys. Eng.

N







Depth in Computer and Systems Eng.

M

Tests, Exams, HW




Basic disciplines in Electric Power Eng.

N







Conduct experiments and interpret data

M

Tests, Exams, HW




Identify, formulate and solve problems

H

Tests, Exams, HW




Design a system, component or process

M

Tests, Exams, HW




Communicate in written and oral form

N







Function as part of a multi-disciplinary team

N







Preparation for life-long learning

N








Ethical issues; safety, health, public welfare

N







Humanities and social sciences

N







Laboratory equipment and software tools

N







Variety of instruction formats

N










Topics Covered:

(number of hours or classes for each)

  1. Probabilistic models and axioms of probability (3)

  2. Sample space, random experiments, counting methods (3)

  3. Independence of events (1.5)

  4. Sample statistics (1.5)

  5. Random variables, probability mass functions, probability density functions, cumulative distribution function, conditional density and distribution functions (6)

  6. Functions of random variables (3)

  7. Expected value, variance and higher moments of a random variable, Chebyshev and Markov inequalities (3)

  8. Hypothesis testing of goodness of fit (1)

  9. Reliability of systems (3)

  10. Computer methods for generating random numbers (1)
  11. CDF and pdf of pairs of random variables (3)


  12. Independence of random variables, conditional CDFs and pdfs and their expectations and correlation (3)

  13. Multiple random variables (2)

  14. Functions of several random variables, pdfs of linear transformations, pdfs of general transformations (3)

  15. Central Limit Theorem (1)







Computer Usage:

Students may use C/C++ or MATLAB in one or two homework assignments







Laboratory Experiences:

    None







Design Experiences:

    None







Independent Learning Experiences:

None







Class/Lab Schedule:

MR 2:00 – 3:20 PM







Contribution to the

(a) College-level mathematics and basic sciences:


2 credit hours

Professional Component:

(b) Engineering Topics (Science and/or Design):

2 credit hours




(c) General Education:

0 credit hours








Prepared by:

John W. Woods

Date:

09-21-2009