ECEN 3810  Introduction to Probability Theory
Catalog Data 
ECEN 3810 (3). Introduction to Probability Theory.
Covers the fundamentals of probability theory, and treats the random variables
and random processes of greatest importance in electrical engineering.
Provides a foundation for study of communication theory, control theory,
reliability theory, optics, and portfolio analysis. 
Credits and Design 
3 credit hours. Required core course. 
Prerequisite(s) 
APPM 2350,
Calculus 3
APPM 2360,
Introduction to Differential Equations with Linear Algebra 
Corequisite(s) 
None. 
Instructor(s) 
Eugene Liu, David Meyer, Francois Meyer, Mahesh Varanasi. 
Textbook 
Sheldon Ross, A First Course In Probability,
8th Edition, Pearson, 2010, ISBN13 9780136033134. 
 

Course Objectives 
For students to:
 Understand and use probability spaces to mathematically describe
signals that exhibit consistent statistical behavior.
 Understand and manipulate mathematical concepts that are used to
quantify the behavior of random variables such as probability density
functions and moments.
 Understand relationships between random variables such as conditional
probability and independence, and limiting behavior of random variables
such as the central limit theorems.

Learning Outcomes 
After taking this course students will be able to recognize and use
the following concepts, ideas, and/or tools:
 Axioms and definitions of probability,
including random variables, independence, and expectation.
 Continuous and discrete probability distributions,
including Bernoulli, binomial, Poisson, Gaussian, and exponential
distributions.
 Random variables, including independence,
correlation, conditional probability, the weak law of large numbers, and
the central limit theorem.

Student Outcomes Addressed 
3a 
3b 
3c 
3d 
3e 
3f 
3g1 
3g2 
3h 
3i 
3j 
3k 
Math /Sci 
Exper iments 
Design 
Teams 
Engr Problems 
Respon sibility 
Oral 
Written 
Engr Solns Impact 
LL Learning 
Contem porary 
Tools 
H 
M 


H 








Topics Covered 
 Axioms and basic definitions of probability
 Combinatorial analysis and counting
 Independence and conditional probabilities
 Random variables: discrete and continuous
 Joint distributions, functions of several random variables
 Conditional probabilities, conditional expectation
 Weak law of large numbers
 Central limit theorem

Last revised: 051811, PM, ARP