# Probability

• ### Song: Central Limit Theorem

A song for use in helping students to recognize when the Central Limit Theorem applies.  Music & Lyrics ©2016 by Greg Crowther from Everett Community College. This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smilesfor the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### The Probability Web

The Probability Web is a collection of probability resources designed to be especially helpful to researchers, teachers, and people in the probability community.  Web page links on this site include probabilty/statistics books and journals, information on mathematics and statistics-based careers, statistical software, teaching resources on probabilty topics, and more.

• ### STatistics Education Web (STEW)

Statistics and probability concepts are included in K–12 curriculum standards—particularly the Common Core State Standards—and on state and national exams. STEW provides free peer-reviewed teaching materials in a standard format for K–12 math and science teachers who teach statistics concepts in their classrooms.

STEW lesson plans identify both the statistical concepts being developed and the age range appropriate for their use. The statistical concepts follow the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K-12 Curriculum Framework, Common Core State Standards for Mathematics, and NCTM Principles and Standards for School Mathematics. The lessons are organized around the statistical problemsolving process in the GAISE guidelines: formulate a statistical question, design and implement a plan to collect data, analyze the data by measures and graphs, and interpret the data in the context of the original question. Teachers can navigate the STEW lessons by grade level and statistical topic.

• ### Analysis Tool(s): JSE Archive of Interactive Computing (includes JAVA Applets)

The Journal of Statistics Education provides a collection of Java applets and excel spreadsheets (and the articles associated with them) from as early as 1998 on this webpage.

• ### Joke: The Knee

A joke to start a discussion on joint probability distributions.  The joke was written in 2018 by Larry Lesser from The University of Texas at El Paso.

A joke to aid in discussing probability density functions for continuous random variables.  The joke was written in 2016 by Judah Lesser an AP statistics student from El Paso, Texas.

• ### Joke: Silver Arrangements

A pun to aid in discussing Stirling's approximation.  The joke was written by Larry Lesser from The University of Texas at El Paso in January 2018.

• ### Joke: A Marginal Joke

A joke to be used in describing how a marginal density is computed from a joint density.  The joke was written in 2017 by Larry Lesser (The University of Texas at El Paso) and Dennis Pearl (Penn State University).

• ### Song: Randomly Select

A song to be used in discussing the value of random selection in sampling and random assignment in experimentation. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 2014 hit “All About that Bass,” by Meghan Trainor. Also, an accompanying video may be found at https://www.youtube.com/watch?v=br-5FtoYfkc

• ### Song: Probability of At Least One

A song to be used in discussing the idea that the probability of at least one can be calculated at 1 minus the probability of none (i.e. the result of one of DeMorgan’s Laws) The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of Sheryl Crow’s 1994 hit song “All I Wanna Do.” Also, an accompanying video may be found at