Download ECE 3910

ECE 3910 - PROBABILITY AND RANDOM VARIABLES
ELECTRICAL & COMPUTER ENGINEERING
Designation: Required for BSEE and BSCmpE
Catalog Description:
Lec. 3, Credit 3
Prerequisites: MATH 2110 and ECE 2010
Introduction to statistical analysis of engineering data. Random experiments, probability, and reliability.
Random variables, distributions, densities, expectation and transformations. Applications to electrical and
computer engineering.
Prerequisites by Topic:
1. Differential and integral calculus
2. Convolution
Textbook(s) and/or Other Required Material(s):
Leon-Garcia, Alberto. Probability, Statistics, and Random Processes for Electrical Engineering, 3rd
Edition, Pearson Prentice Hall, 2008
Reference Material(s): None
Topics Covered:
1. Electrical and computer engineering applications such as system reliability, component tolerances, and
telecommunications channels. (2 hours)
2. Statistical analysis of engineering data. (1 hour)
3. Concepts of probability through set theory. (12 hours)
4. Counting methods and permutations and combinations. (3 hours)
5. Random variables, distribution and density functions. (10 hours)
6. Functions and transformations of random variables. (5 hours)
7. Multiple random variables, joint distribution and density functions, and sums of random variables.
(12 hours)
Class/Laboratory Schedule:
Lecture: 3 hrs/week
Laboratory: 0 hrs/week
Recitation: 0 hrs/week
Other: 0 hrs/week
Course Objectives and Relationship to Program Education Objectives:
1. To introduce the fundamentals of statistics and probability, so that
(a) Students can analyze empirical data and building a probability model for systems. (EE: A;
CmpE: A)
(b) Students are familiar with the axioms of probability and various counting methods. (EE: A;
CmpE: A)
(c) Students can apply concepts such as conditional probability, independence of events and
sequential events. (EE: A; CmpE: A)
2. To introduce the fundamentals of random variables so that students
(a) Understand and are able to utilize cumulative distribution functions (cdf) and probability density
functions (pdf). (EE: A; CmpE: A)
(b) Are familiar with common discrete and continuous random distribution functions. (EE: A;
CmpE: A)
(c) Can calculate the first- and second-order statistics of random variables. (EE: A; CmpE: A)
(d) Are familiar with techniques applicable to multiple random variables. (EE: A; CmpE: A)
(e) Are familiar with the law of large numbers and the central limit thereon. (EE: A; CmpE: A)Course
Objectives and Relationship to Program Education Objectives - Continued
ECE 3910
Page 2
3.
4.
To apply these fundamentals to various aspects of electrical engineering so that students:
(a) Are aware of applications in system reliability, component tolerance and communication systems.
(EE: A; CmpE: A)
(b) Can apply this knowledge to the analysis of system reliability. (EE: A; CmpE: A)
To provide the student with the fundamentals of probability and random variables so that students are
prepared:
(a) To take graduate-level courses requiring such background. (EE: A; CmpE: A)
(b) For future courses in random processes (EE: A; CmpE: A)
(c) To take more senior-level courses in telecommunications (ECE 4710 and ECE 4720). (EE: A;
CmpE: A)
Course Outcomes and Relationship to Program Outcomes:
A student completing this course should, at a minimum, be able to:
1. Given a set of empirical data, be able to determine the first- and second-order statistics of the data.
(EE: 1, 2, 13; CmpE: 1, 2, 13)
2. Given a system consisting of series and parallel components having known reliability, be able to
calculate the system reliability. (EE: 1, 5, 13, 14; CmpE: 1, 5, 13, 14)
3. Be able to apply the various counting methods (with and without replacement and with and without
ordering) as appropriate in determining probability of Bernoulli experiments. (EE: 1, 5, 13; CmpE: 1,
5, 13)
4. Given either the cdf or pdf of a random variable, be able to find one from the other. (EE: 1, 5, 12, 13;
CmpE: 1,5,12,13)
5. Given either the cdf or pdf of a random variable, be able to calculate the first- and second-order
statistics of the random variable. (EE: 1, 5, 12, 13; CmpE: 1, 5, 12, 13)
6. Given either the cdf or pdf of a random variable, be able to calculate the probability the random
variable will lie within a specified range. (EE: 1, 5, 12, 13; CmpE: 1, 5, 12, 13)
7. Given a binary communication channel corrupted by additive Gaussian noise, be able to calculate
probability of errors and a posteriori probabilities. (EE: 1, 5, 12, 13, 14; CmpE: 1, 5, 12, 13, 14)
8. Given a set of independent random variables, be able to determine the joint probabilities and the firstand second-order statistics of their sums. (EE: 1, 5, 12, 13; CmpE: 1, 5, 12, 13)
Outcomes Assessment Tools:
Outcome Nos. 1 - 8: 4 in-class exams plus 1 final exam
Outcome Nos. 1 - 8: Graded homework assignments
Contribution of Course to Meeting the Professional Component:
Math and Basic Science: 1 hr.
General Education: 0 hrs.
Engineering: 2 hrs. (Design: 0 hrs.)
Other: 0 hrs.
Prepared by: Dr. Jeffrey Austen
Revised: September 24, 2008