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  • Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, the order on which the dispersion of the relative frequency diminishes. Key words: probability, law of large numbers, simulation, estimation

    Includes project file for Minitab and coding for a dice rolling simulation.

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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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  • Explore the functionality of your scientific calculator.

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  • 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
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  • 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
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  • A mathematical word processor that includes an easy-to-use computer algebra system (MuPad). Products include Scientific Wokplace, Scientific Word, Scientific Notebook, and MuPad Pro. Student version are available.

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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 program visualizes the effects of outliers to regression lines. The user may pick up a point with the mouse and move it across the chart. The resulting regression line is automatically adjusted after each movement, showing the effect in an immediate and impressive way. The program Leverage allows one to experiment with the leverage effect. You can create a random sample of data noisy points on a line. Dragging one of the points away from the regression line immediately shows the effect, as the regression line is recalculated and moves according to the current data set. Not online: user has to download the program.

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  • This program has been written to explore the relationship between the data points and the error surface of the regression problem. On one hand you can learn how to represent a line in two different spaces ({x,y} and {k,d}), and on the other hand you see that solving the regression problem is nothing else than finding the minimum in the error surface.

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  • 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.
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