Probability Measures

  • A song to teach various concepts in probability. Written by Mary Pat Campbell for Mathcamp 2002 at Colorado College. May be sung to the tune of "Take a Chance on Me" by ABBA. Musical accompaniment realization by Joshua Lintz and vocals by Mariana Sandoval from University of Texas at El Paso.

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  • Song is about formal constructions of probability theory. May be sung to the tune of "Strawberry Fields" by John Lennon and Paul McCartney. Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.
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  • The t-distribution activity is a student-based in-class activity to illustrate the conceptual reason for the t-distribution. Students use TI-83/84 calculators to conduct a simulation of random samples. The students calculate standard scores with both the population standard deviation and the sample standard deviation. The resulting values are pooled over the entire class to give the simulation a reasonable number of iterations. This document provides the instructor with learning objectives, context, mechanics, follow-up, and evidence from use associated with the in-class activity.
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  • This site presents several photographs from real life that demonstrate natural statistical concepts. Each picture shows a statistical distribution made by some pattern occuring in everyday life. An explanation of each picture tells what distribution is being represented and how.
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  • This applet generates confidence intervals for means or proportions. The options for confidence intervals for means include "z with sigma," "z with s," or "t." The options for confidence intervals for proportions are "Wald," "Adjusted Wald," or "Score." Users set the population parameters, sample size, number of intervals, and confidence level. Click "Sample," and the applet will graph the intervals. Intervals shown in green contain the true population mean or proportion, while intervals in red do not. The true mean or proportion is shown by a blue line. The applet displays the proportion of intervals containing the population parameter for each sample and a running total of all the samples. Users can also click on a particular interval to display the numerical interval or sort the displayed confidence intervals from smallest to largest. This applet is part of a collection designed to accompany the textbook "Investigating Statistical Concepts, Applications, and Methods" (ISCAM) and is used in Exploration 4.3 on page 327, Investigation 4.3.6 on page 331, and Exploration 4.4 on page 350. This applet also supplements "Workshop Statistics: Discovery with Data," 2nd edition, Activity 19-5 on page 403. Additional materials written for use with these applets can be found at http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/16_cireview_bc322_2.doc and http://www.mathspace.com/NSF_ProbStat/Teaching_Materials/rowell/final/15_sampdistreview_bc322_1.doc.
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  • This applet displays various distributions and allows the user to experiment with the parameters to see the effects on the curve.

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  • Submitting your spotlight presentation from USCOTS 2005 to CAUSEweb is an easy process, and you are in a prime position to submit your work! What better way to have your work showcased than in a peer-reviewed repository of contributions to statistics education? This Webinar from January 2006 provided an opportunity to talk about how to prepare your USCOTS spotlight for submission to CAUSEweb and to discuss the benefits of submission.

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  • A cartoon to use at the end of a class period when the instructor was rushed to finish. Cartoon by John Landers (www.landers.co.uk) based on an idea from Dennis Pearl (The Ohio State University). Free to use in the classroom and on course web sites.
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  • This website serves as an online textbook for introductory statistics, covering topics such as summarizing and presenting data, producing data, variation and probability, statistical inference, and control charts.
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  • This website contains more real analysis, general topology and measure theory than actual probability. It is more about the foundations of probability theory, than probability itself. In particular, it is a very suitable resource for anyone wishing to study the Lebesgue integral. These tutorials are designed as a set of simple exercises, leading gradually to the establishment of deeper results. Proved Theorems, as well as clear Definitions are spelt out for future reference. These tutorials do not contain any formal proof: instead, they will offer you the means of proving everything yourself. However, for those who need more help, Solutions to exercises are provided, and can be downloaded.
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