Moments of Continuous Probability Density Functions (PDFs)

Abstract

A common topic in Calculus-based Probability and Statistics is Probability Density Functions (PDFs) and the immediate application discussed in most classes is computations of mean and standard deviation. In this activity, we use POGIL to build upon previous knowledge of moments, mean, and standard deviation in the context of Probability Mass Functions (PMFs) for discrete sample spaces in order to introduce students to how they can find the mean and standard devation for PDFs in the case of continuous sample spaces. This activity does assume students have familiarity with improper integrals and integration methods from Calculus.

Level: Undergraduate
Setting: Classroom
Activity Type: Learning Cycle
Discipline: Calculus
Course: Calculus
Keywords: integration, improper integrals, moments, mean, and standard deviation