Resource Library

This Compendium describes distributions appropriate for the modeling of random data. The number of distributions (56) is large, including: 1. Continuous distributions (30), (Symmetric (11) and Skewed (19)) 2. Continuous binary mixtures(17), 3. Discrete distributions (5), 4. Discrete binary mixtures (4), All formulas are shown in their fully-parametrized form, not the standard form. Many of the formulas given are seldom described. Random variate generation is included where feasible.

This site discusses types of data, stem and leaf plots, mean and median, histograms, and barcharts. Exercises are also provided, as well as their corresponding answers.

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.

Pseudo random number generators (PRNG) start with a seed value and will eventually repeat all the numbers they generate in exactly the same order. Putting in the same seed value will give precisely the same set of random numbers. On large scale Monte Carlo simulations (depends on generation of multiple random numbers), care has to be taken to make sure that the PRNG cycle is significantly longer than the quantity of random numbers needed or the pattern in the PRNG cycle can show up as an error producing pattern in the simulation results.

This page provides an example of pseudo random number generators (PRNG) creating spread spectrum broadcasts and signals for encryption and decryption of wireless transmissions.

This lesson plan uses the Birthday Paradox to introduce basic concepts of probability. Students run a Monte Carlo simulation using the TI-83 graphing calculator to generate random dates, and then search for matching pairs. Students also perform a graphical analysis of the birthday-problem function. Key Words: Permutations; Explicit Function; Recursive Function; Modeling.

This example is designed to test whether religiosity is correlated with optimism. The page describes the study, has a link to the data set, and describes the method of analysis. Analysis includes ANOVA and regression.

This set of exercises asks students to model relationships and test them based on the chi-square distribution. The data used is based on testosterone levels and delinquency rate of American military men.

This correlation and regression example compares performance on reading comprehension questions to performace on the SAT. It also compares those who read the passage referred to by the questions to those who did not. Exercise questions and answers are also provided.