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Functions of Random Variables

  • A cartoon with a neat double pun that can be a nice vehicle to discuss how the expectations of non-linear functions of a random variable is not the same as the function of the expectations. The cartoon was used in the February 2019 CAUSE cartoon caption contest and the winning caption was written by Joseph Gerda from College of the Canyons. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • 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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  • In this demonstration a scatterplot is displayed and you draw in a regression line by hand. You can then compare your line to the best least squares fit. You can also try to guess the value of Pearson's correlation coefficient.
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  • This tutorial on Random Variables helps students understand the definition of random variables, recognize and use discrete random variables, recognize and use continuous random variables, and solve exercise problems using random variables.
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  • This module is a short quiz which gives a review/assessment of the main concepts for this refresher course. At the bottom, there is a grading button to rate the understanding of the material.
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  • This free online video program, "demonstrates how to determine the probability of any number of independent events, incorporating many of the same concepts used in previous programs. An interview with a statistician who helped to investigate the space shuttle accident shows how probability can be used to estimate the reliability of equipment."
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  • This is a "Building Block" for the Buffon Needle problem. The source code and compile code are included as well as separate files for each. Users able to test the applet to determine if it meets their needs.

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  • This applet simulates rolling dice and displays the outcomes in a histogram. Students can choose to roll 1, 2, 6, or 9 dice either 1, 10, 20, or 100 times. The outcome studied is the sum of the dice and a red line is drawn on the histogram to show expected number of occurences of each outcome.

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