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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, ISBN-13 978-0-13-603313-4.
  
Course Objectives For students to:
  1. Understand and use probability spaces to mathematically describe signals that exhibit consistent statistical behavior.
  2. Understand and manipulate mathematical concepts that are used to quantify the behavior of random variables such as probability density functions and moments.
  3. 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:
  1. Axioms and definitions of probability, including random variables, independence, and expectation.
  2. Continuous and discrete probability distributions, including Bernoulli, binomial, Poisson, Gaussian, and exponential distributions.
  3. 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
  1. Axioms and basic definitions of probability
  2. Combinatorial analysis and counting
  3. Independence and conditional probabilities
  4. Random variables: discrete and continuous
  5. Joint distributions, functions of several random variables
  6. Conditional probabilities, conditional expectation
  7. Weak law of large numbers
  8. Central limit theorem

Last revised: 05-18-11, PM, ARP