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ECEN 303: Random Signals and Systems
Fall 2009
Instructor:
Dr. JeanFranc
¸ois Chamberland
Assistant Professor
Department of Electrical and Computer Engineering
Office:
Room 244F, WERC
Email:
chmbrlnd@ece.tamu.edu (Subject: ECEN 303)
Phone:
(979) 8456204
Web:
http://www.ece.tamu.edu/˜chmbrlnd/Courses/
Office Hours:
Monday, 3:00–4:30 p.m.
Course Outline
This course will introduce the student to the fundamental concepts of probability theory applied to engi
neering problems. Its objective is to develop the ability to construct and exploit probabilistic models in a
manner that combines intuition and mathematical precision. The proposed treatment of probability includes
elementary set operations, sample spaces and probability laws, conditional probability, independence, and
notions of combinatorics. A discussion of discrete and continuous random variables, common distributions,
functions and expectations forms an important part of this course. Transform methods, limit theorems, con
vergences and bounding techniques are also covered. In particular, special consideration is given to the law
of large numbers and the central limit theorem. Many examples from engineering, science, and statistics
will be provided.
Major Goals
1. Review basic notions of set theory and simple operations such as unions, intersections, differences
and De Morgan’s laws. Discuss cartesian products and simple combinatorics. Go over the counting
principle, permutations, combinations and partitions.
2. Introduce sample spaces, probability laws and random variables. Distinguish between events and
outcomes, and illustrate how to compute their probabilities.
3. Present the concepts of independence and conditional probabilities. Study the total probability the
orem and Bayes’ rule. Provide examples of these important results applied to tangible engineering
problems.
4. Understand mathematical descriptions of random variables including probability mass functions, cu
mulative distribution functions and probability density functions. Become familiar with commonly
encountered random variables, in particular the Gaussian random variable.
5. Introduce the notions of expectations and moments, including means and variances. Calculate mo
ments of common random variables. Characterize the distributions of functions of random variables.
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View Full Document6. Explore the properties of multiple random variables using joint probability mass functions and joint
probability density functions. Understand correlation, covariance and the correlation coefficient. Dis
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 Fall '07
 Chamberlain

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