Multivariate Distributions

  • This is a three day lesson plan. The first day is an introduction to concepts in probability. The second day is an application of probability in the field of genetics. The third day is a time for students to expand their understanding of probability and genetics via short research project. The site includes resources, advice, and notes to the teacher. Probability topics include: law of large numbers, simple and compound events, sample size, sample space, and more.
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  • This website provides the URL of a Java applet and steps for using it. Here, students can manipulate the size of the circle and the rectangle to explore the probability that a point in the rectangle is also in the circle.
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  • This activity addresses the concept of sample space. It provides a multi-step procedure and three handouts, which accompany the activity. It addresses events and the availability misconception as well as grouping and forming committees.
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  • This PowerPoint presentation dicusses general concepts of confidence intervals and interprets confidence intervals for a mean, difference in two means, and the relative risk. The original presenation is available for download.
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  • This PowerPoint lecture presenation explains confidence intervals for a mean when using a small sample. It discusses the t-distribution, compares the t-statistic to the z-statistic, and provides an example of a small sample confidence interval. The original presentation is available for download.
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  • This article describes an activity that illustrates contingency table (two-way table) analysis. Students use contingency tables to analyze the "unusual episode" (the sinking of the ocean liner Titanic)data (from Dawson 1995) and attempt to use their analysis to deduce the origin of the data. The activity is appropriate for use in an introductory college statistics course or in a high school AP statistics course. Key words: contingency table (two-way table), conditional distribution

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  • This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level. Students are expected to approximate the solution through simulation before solving it exactly. They are also expected to employ graphical as well as algebraic problem-solving strategies, in addition to their simulation analyses. Finally, students are asked to explain intuitively why it makes sense for the probabilities to change as they do. Key words: simulation, probability, geometry, independence, bivariate normal distribution
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  • The program DistCalc calculates probabilities and critical values for the most important distributions. The purpose of this program is to show the concept of critical values and the replacement of printed distribution tables. The Distribution Calculator offers calculations for the normal distribution, the t distribution, the chi-square distribution, and the F distribution.

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  • This article discusses a project-based approach to teaching statistics. An appendix contains a list of 20 projects that have been successfully assigned.
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  • This data archive contains data sets divided into the following categories: Astronomy, Biology, Education, Geography, Social Sciences, Sports, Transportation, Weather, and Miscellaneous. The datasets can be viewed as an html page or downloaded into Excel spreadsheets.
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