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Elementary Probability

  • The following applet allows you to simulate the Shannon experiment, an experiment aimed at determining the entropy of an English letter (the amount of information in bits that we obtain on the average when we learn one letter of English). The simulation will calculate the amount of entropy for you when you are finished guessing the letters.
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  • This applet is programmed to illustrate the code-breaking process using the Vigenere encryption as the code. The Vigenere encryption is broken by comparing histograms of various frequencies until the correct guess is obtained. A wrong guess for the period p leads to relatively flat histograms. The code breaker in this case repeats the analysis with a new trial period.
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  • This applet illustrates the codebreaking process entitled Rectangular Transposition Encryption System.
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  • This applet illustrates the codebreaking process using a chi-squared process.
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  • This site shows the ISI's alphabetical list of technical terms in statistics showing the translation in a number of languages.
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  • This site provides definitions and examples for the following topics: Graphical displays (stemplots, histograms, boxplots, scatterplots), Numerical Summaries (mean, median, quantiles, variance, standard deviation), Normal Distributions (assessing normality, normal probability plots), Categorical Data (two-way tables, bar graphs, segmented bar graphs), Linear regression (least-squares, residuals, outliers and influential observations, extrapolation), Correlation (correlation coefficient, rŒ_), Inference in Linear Regression (confidence intervals for intercept and slope, significance tests, mean response and prediction intervals), Multiple Linear Regression (confidence intervals, tests of significance, squared multiple correlation), ANOVA for Regression (analysis of variance calculations for simple and multiple regression, F statistics), Experimental Design (experimentation, control, randomization, replication), Sampling (simple, stratified, and multistage random sampling), Sampling in Statistical Inference (sampling distributions, bias, variability), Probability Models (components of probability models, basic rules of probability), Conditional Probability (probabilities of intersections of events, Bayes' formula), Random variables (discrete, continuous, density function), Mean and Variance of Random Variables (definitions, properties), Binomial Distributions (counts, proportions, normal approximation), Sample Means (mean, variance, distribution, Central Limit Theorem), Confidence Intervals (inference about population mean, z and t critical values), Tests of Significance (null and alternative hypotheses for population mean, one-sided and two-sided z and t tests, levels of significance, matched pairs analysis), Comparison of Two Means (confidence intervals and significance tests, z and t statistics, pooled t procedures), Inference for Categorical Data (confidence intervals and significance tests for a single proportion, comparison of two proportions), Chi-square Goodness of Fit Test (chi-square test statistics, tests for discrete and continuous distributions), Two-Way tables and the Chi-Square test (categorical data analysis for two variables, tests of association).
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  • This site gives a definition and an example of stem and leaf plots.
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  • This site gives a definition and an example of histograms.
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  • This site give a definition and an example of boxplots. Topics include outliers, medians, as well as lower and upper quartiles.
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  • This site gives a definition and an example of scatterplots. Topics include positive and negative association.
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