An intuitive, application-based, simulation-driven approach to teaching probability and random processes

Abstract

Probability and random processes is considered by students to be conceptually one of the most difficult subjects in the undergraduate electrical and computer engineering curriculum. There are numerous reasons for this difficulty encountered by the students. First off, humans are not innately good at probabilistic intuition. Traditionally, this subject has been introduced in a very abstract manner without emphasis on real-world applications from electrical and computer engineering discipline. In addition, extensive use of interactive simulation and visualization tools, offering an alternative way of developing probabilistic intuition, is usually missing from traditional course offerings. This paper presents a unique pedagogical approach to teaching an introductory probability course offered to electrical and computer engineering juniors. The salient features of the proposed pedagogical approach include more emphasis on real-world electrical and computer engineering problems that show the applications of abstract probabilistic concepts; extensive hands-on and interactive MATLAB® simulations of real-world electrical and computer engineering problems that are tightly integrated into the curriculum; highlighting the frequentist approach to build probabilistic intuition using simulations; concrete examples showing how naive probabilistic intuition can be erroneous and how to develop correct probabilistic intuition based on systematically modeling, simulating, and analyzing a problem; and application-based simulations driving the abstract theory rather than the other way around. This pedagogical approach was implemented in a course offered to electrical and computer engineering undergraduates at Purdue University Northwest. The paper presents a concrete example illustrating how the salient features of the proposed pedagogical approach were implemented as part of this course and student data from the courses to validate the efficacy of the proposed approach.