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# Non-symbolic math

• ### Analysis Tool: Empirical Cumulative Distribution

This applet allows the user to enter data, then returns the values of empirical cumulative distribution function by sorting the data and reporting the height of the curve at each point. It does not show the graph.

• ### The Cramer-Rao Lower Bound

This page introduces the Cramer-Rao lower bound, discusses it's usefulness, and proves the inequality.
• ### Theoretical Underpinnings of the Bootstrap

This page discusses the theory behind the bootstrap. It discusses the empirical distribution function as an approximation of the distribution function. It also introduces the parametric bootstrap.
• ### Advanced Statistics - Biology 603 - Lectures

This site provides links to lecture outlines for an upper-level statistics class. Topics include hypothesis testing, ANOVA and regression.
• ### The Gambler's Ruin Problem

This applet allows you to experience the fate of a gambler by simulating the whole gambling session in a matter of seconds. The applet plots the successive rises and falls of the capital during the whole duration of the game. It also displays the maximum and minimum values attained by the capital during the session and allows you to get precise information (by clicking at a point of the histogram) of the amount of capital after that particular bet.
• ### Let's Make a Deal

This page has links to an explanation of the applet and to the applet itself. It is a simulation of the T.V. game show. There are three doors to choose from and after making a choice, one of the other doors is revealed. The player can choose to pick the other unopened door or stay with their original choice. Afterwards the statistics of previous contestants are shown. (Note: the applet statistics are inaccurate)
• ### Introduction to Cryptography: Games and Programs

This is a collection of applets including Let's Make A Deal, Let's Make a Deal II, Monkey Words, Entropy, Vigenere, Rectangular Transposition, and Monoalphabetic Substitution.
• ### Let's Make a Deal II

This applet doesn't have more explanation than - Let's Make a Deal II- An applet to demo at the UCLA conference. It has statistics for a number of tries at a time with choices for whether or not the host knows what is behind the door and whether or not the contestant switches doors after primary choice.
• ### Shannon's Experiment to Calculate the Entropy of English

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.
• ### Breaking The Vigenere Encryption System

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.