Probability Density Functions (PDFs)

Abstract

In Probability and Statistics classes (Calculus-based), it is often the case that classes are taught with discrete (finite or countably infinite) sample spaces on one side and continuous (uncountably infinite) sample spaces on the other side, presented as separate concepts. One problem with this idea is that fundamentally they are related to one another, as verified in deeper Probability Theory as well as connections we see in later statements like the Central Limit Theorem. I am aiming to collaborate in developing a POGIL activity to be used in bridging the gap between discrete and continuous sample spaces, focusing on the PMFs and PDFs used in computing probability.

Level: Undergraduate
Setting: Classroom
Activity Type: Learning Cycle
Discipline: Mathematics, Statistics
Course: Calculus-based Probability and Statistics
Keywords: Probability Density Functions, Probability Mass Functions