# Random Variables

• ### Is He Guilty?

This PowerPoint presentation evaluates type I errors in civil trials compared to criminal trials as well as provides an example of a hypothesis test and its components. The original presenation is available for download.
• ### Hypothesis Testing

This PowerPoint lecture presentation discusses comparing the means of two dependent populations using the paired T-test and defines the concepts of this hypothesis test. The original presentation is available for downloading.
• ### Star Library: The Role of Probability in Discrimination Cases

An important objective in hiring is to ensure diversity in the workforce. The race or gender of individuals hired by an organization should reflect the race or gender of the applicant pool. If certain groups are under-represented or over-represented among the employees, then there may be a case for discrimination in hiring. On the other hand, there may be a number of random factors unrelated to discrimination, such as the timing of the interview or competition from other employers, that might cause one group to be over-represented or under-represented. In this exercise, we ask students to investigate the role of randomness in hiring, and to consider how this might be used to help substantiate or refute charges of discrimination. Key words: Probability distribution, binomial distribution, computer simulation, decision rules
• ### DAU StatRefresher: Random Variables

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.
• ### DAU StatRefresher: Final Test

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.
• ### Probability Spaces

This online, interactive lesson on probability spaces provides examples, exercises, and applets that cover conditional probability, independence, and several modes of convergence that are appropriate for random variables. This section also covers probability space, the paradigm of a random experiment and its mathematical model as well as sample spaces, events, random variables, and probability measures.

• ### Sufficient Statistics

This page introduces the definition of sufficient statistics and gives two examples of the use of factorization to prove sufficiency.
• ### Categorical Data

This site gives a definition and an example of categorical data. Topics include two-way tables, bar graphs, and segmented bar graphs.
• ### Linear Regression

This site gives an explanation, a definition and an example of linear regression. Topics include least-squares, residuals, extrapolation, outliers, and influential observations.

• ### Correlation

This site gives an explanation, a definition and an example of correlation. Topics include correlation coefficient and rŒ_.