Special Probability Mass Functions (PMFs)

Abstract

In this activity, students explore named probability mass functions (PMFs) over discrete sample space, namely the Discrete Uniform, Bernoulli, Binomial, and Geometric distributions for a Calculus-based Probability and Statistics undergraduate course. A special emphasis in this activity is not only identifying the relevant PMFs, but also brainstorming conditions needed for the PMFs to apply. This emphasis is especially helpful for motivating students in majors outside of mathematics.

The activity is designed specifically to be following introduction to PMFs, including modeling a PMF for a given situation, as well as computing mean and standard deviation for a given PMF. With the Geometric distribution in particular, it may be helpful to be really familiar with the ideas behind the mean and standard deviation computations for the specific PMFs, as well as summation formulas.

Level: Undergraduate
Setting: Classroom
Activity Type: Learning Cycle
Discipline: Statistics
Course: Probability and Statistics
Keywords: calculus, discrete uniform distribution, Bernoulli distribution, binomial distribution, geometric distribution, probability mass function, mean, standard deviation