College --Undergrad Upper Division

  • This website is provides an online text version of Grinstead & Snell's "Introduction to Probability" as well as supplemental reference information.

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  • Using cooperative learning methods, this lesson introduces distributions for univariate data, emphasizing how distributions help us visualize central tendencies and variability. Students collect real data on head circumference and hand span, then describe the distributions in terms of shape, center, and spread. The lesson moves from informal to more technically appropriate descriptions of distributions.
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  • Compared to probability calculators, the traditional format of distribution tables has the advantage of showing many values simultaneously and, thus, enables the user to examine and quickly explore ranges of probabilities. This webpage includes a list of distributions and tables, including the standard normal (Z) table, student's t table, chi-square table, and F distribution tables. An animation of the density function and distribution function is shown above each distribution table to demonstrate the effects changing degrees of freedom and significance levels have on the shape of a distribution.

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  • This text based website provides an explanation of some coincidences that are often discussed. It gives an explanation of the birthday problem along with a graphic display of the probability of birthday matches vs. the number of people included. It also discussess other popular coincidences such as the similarities between John F. Kennedy and Abraham Lincoln. It goes on to discuss steaks of heads and tails along with random features of stocks and the stock market prices.
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  • This applet relates the pdf of the Normal distribution to the cdf of the Normal distribution. The graph of the cdf is shown above with the pdf shown below. Click "Move" and the scroll bar will advance across the graph highlighting the area under the pdf in red. The z-score is shown as well as the probability less than z (F(z)) and the probability greater than z (1-F(z)).
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  • This applet draws one-dimensional Brownian motion. Click the mouse in the window to start zooming. Click again to stop. Since Brownian motion is self-similar in law, all of the zoomed pictures look the same.
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  • This page computes a variety of descriptive statistics and creates a stem and leaf plot. Enter data in the text area, specify a delimiter (Space, Return, Tab, New line), and click "Compute". The page returns sample size, mean, median, trimmed mean, trimean, minimum, maximum, range, first quartile, third quartile, semi-interquartile range, standard deviation, variance, standard error of the mean, skew, and kurtosis. Key Word: Calculator; Summary Statistics.

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  • This applet draws a Gamma process (a stochastic process with independent increments X(s + t) - X(s).) Click the mouse in the window to start zooming. Click again to stop. The total increase occurs at a countable set of jumps. The simulation gives some idea of this.
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  • This page introduces the Kolmogorov-Smirnov test, gives background and procedures for the test, and provides a calculation page which allows users to enter their own data and perform the test.

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  • This page introduces contigency tables with an example on fruit trees and fire blight. Two calculators are provided that allow users to enter their own contigency table and test for treatment effects. The first calculator performs Fisher's Exact Test on a 2x2 tables. The second performs a chi-square test on up to a 9x9 table.

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