Simulation

  • 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.
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  • 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.
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  • 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.
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  • 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.
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  • This page provides an example of pseudo random number generators (PRNG) creating spread spectrum broadcasts and signals for encryption and decryption of wireless transmissions.
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  • 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.
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  • An independent, nonpartisan resource on trends in American public opinion. Gives examples of recent polls, margins of error, questions asked, and sample sizes.
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  • This is a virtual applet, which models repeaded coin tossing by a random number generator. It allows you to change the number of tosses as well as runs and records your results.
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  • 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.
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  • As described in the web page itself: "This document was prepared as an illustration of the use of both t tests and correlation/regression analysis in drawing conclusions from data in an actual study." The study compares athletic performance of swimmers that are optimists vs. pessimists.
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