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This is an example of "growing" a decision tree to analyze two possible outcomes. The tree's branches examine the two possible conditions of employee drug use with corresponding probabilities. This example looks at the final outcome probabilities of being correctly and incorrectly identified versus testing accuracy.

This page explores Benford's Law: For naturally occurring data, the digits 1 through 9 do not have equal probability of being the first significant digit in a number; the digit 1 has greater odds of being the first significant digit than the others. This law can be used to catch tax fraud because truly random numbers used by embezzlers do not meet this condition.

This page explores Benford's law and the Pareto Principle (or 80/20 rule). Benford's law may also have a wider meaning if the digits it evaluates are considered ranks or places. The digit's probability of occurring could be considered the relative share of total winnings for each place (1st through 9th). In other words, 1st place would win 30.1%, 2nd place 17.6%, 3rd 12.5%,... 9th place 4.6% of the available rewards. The normalized Benford curve could be used as a model for ranked data such as the wealth of individuals in a country. To determine if the Benford model gives results similar to those of the Pareto principle we use the normalized Benford equation in a computer program.

This page shows how elements of a systems can be eliminated as causes in problem troubleshooting. The principles of twenty questions are frequently used in the business world to conduct computerized searches of massive data bases. These are called a binary searches and are one of the fastest search methods available. To conduct binary searches, data must be sorted in order or alphabetized. The computer determines which half of the list contains the item. The half containing the item is divided in half again and the process repeated until the item is found or the list can no longer be divided. Problem solvers should avoid focusing on the cause and instead ask which elements of the system can be eliminated as causes.

Using a parameter it's possible to represent a property of an entire population with a single number instead of millions of individual data points. There are a number of possible parameters to choose from such as the median, mode, or interquartile range. Each is calculated in a different manner and illuminates the data from a different point of view. The mean is one of the most useful and widely used and helps us understand populations. A population is simulated by generating 10,000 floating point random numbers between 0 and 10. Sample means are displayed in histograms and analyzed.

This activity provides students with 24 histograms representing distributions with differing shapes and characteristics. By sorting the histograms into piles that seem to go together, and by describing those piles, students develop awareness of the different versions of particular shapes (e.g., different types of skewed distributions, or different types of normal distributions), that not all histograms are easy to classify, that there is a difference between models (normal, uniform) and characteristics (skewness, symmetry, etc.). Key words: Histogram, shape, normal, uniform, skewed, symmetric, bimodal

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

Residual plots and other diagnostics are important to deciding whether or not linear regression is appropriate for a set of data. Many students might believe that if the correlation coefficient is strong enough, these diagnostic checks are not important. The data set included in this activity was created to lure students into a situation that looks on the surface to be appropriate for the use of linear regression but is instead based (loosely) on a quadratic function. Key words: regression, residuals

This course in Statistical Mechanics features problem sets and exams. Basic principles examined include: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy; postulates of classical statistical mechanics, microcanonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas; quantum statistical mechanics; Fermi and Bose systems; and interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

This course features a full set of lecture notes and problem sets introducing students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.