Multivariate Distributions

  • How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview.

    By the end of this course, you’ll master the fundamentals of probability and random variables, and you’ll apply them to a wide array of problems, from games and sports to economics and science.  This course includes 62 interactive quizzes and more than 400 probabilty-based problems with solutions.  Access to this course requires users to sign up for a free account.

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  • This page supports an in-class exercise that highlights several key Bayesian concepts. The scenario is as follows: a large paper bag contains pieces of candy with wrappings of different color, and we are interested in learning about the unknown proportion of yellow-wrapped pieces of candy. After completing the exercises, we will be familiar with the following concepts and ideas: probability distributions can quantify degree of belief, prior distribution, posterior distribution, sequential updating, conjugacy, Cromwell’s Rule (http://en.wikipedia.org/wiki/Cromwell's_rule), the data overwhelm the prior, Bayes factors, Savage-Dickey density ratio, sensitivity analysis, coherence.

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  • This resource is designed to provide new users to R, RStudio, and R Markdown with the introductory steps needed to begin their own reproducible research. Many screenshots and screencasts (with no audio) will be included, but if further clarification is needed on these or any other aspect of the book, please create a GitHub issue here or email me with a reference to the error/area where more guidance is necessary.  It is recommended that you have R version 3.3.0 or later, RStudio Desktop version 1.0 or higher, and rmarkdown R package version 1.0 or higher. 

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  • 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.

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  • 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).

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  • This activity uses student's own data to introduce bivariate relationship using hand size to predict height. Students enter their data through a real-time online database. Data from different classes are stored and accumulated in the database. This real-time database approach speeds up the data gathering process and shifts the data entry and cleansing from instructor to engaging students in the process of data production.

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  • This activity will allow students to familiarize themselves with technology and its use in calculating marginal, conditional, and joint distributions, as well as making conclusions from these tabular and graphical displays. The corresponding data set 'Pizza Data' is located at the following web address: http://www.causeweb.org/repository/ACT/PIZZA.TXT
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  • A cartoon to teach about the importance of blinding the researcher to which comparison group the subjects are in. 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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  • A cartoon to teach about the use of placebos in experiments. 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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  • A cartoon to teach about finding the moments of a distribution. 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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