By Xiaoxia Champon (North Carolina State University), Dr. Justin Post (North Carolina State University)
Information
Convergence of random variables is a notoriously difficult concept for students to understand and for teachers to explain. We demonstrate three commonly taught convergence concepts: in distribution/law, in probability, and almost surely through the use of interactive Shiny Applications. After many years of teaching with static illustrations, these tools, which provide dynamic visuals of the concepts, were developed to help students better understand the intuition behind which characteristics of a random sequence are important for convergence properties. These tools allow for multiple random sequences with known features to be simulated and the behavior changes of the random sequences to be explored through visual representations. While convergence in probability is generally only taught in the theoretical courses for statistics majors, the convergence in distribution/law topic is taught in most introductory statistics courses (via the central limit theorem). These applications should be useful for both the introductory audience and the statistics focused audience, although the latter may find them more beneficial. We advocate the use of these tools and other visuals as a hands-on activity that can improve the conceptual understanding of these difficult topics by allowing the teacher and students to visually inspect the underlying attributes associated with the theoretical concepts.
https://github.com/XiaoxiaChampon/ConvergenceConcepts
https://jbpost2.github.io/Intro_Data_Science_Project_USCOTS_2023/