# Elementary Probability

• ### STATISTICS FOR MOLECULAR BIOLOGY AND BIOINFORMATICS

A computer intensive introductory course for graduate students. A veritable online course with Powerpoint and Excel downloadable files for viewing. Also provides related outside links for further investigation on related topics.
• ### Bernoulli Trials

This online, interactive lesson on Bernoulli provides examples, exercises, and applets that cover binomial, geometric, negative binomial, and multinomial distributions.
• ### Patterns in Nature

This site provides a collection of applets and their descriptions. Some of the titles include the Monte Carlo Estimation of Pi, Can You Beat Randomness?, One-Dimensional Random Walk, Two-Dimensional Random Walk, The Anthill and Molecular Motion, Diffusion Limited Aggregation, The Self-Avoiding Walk, Fractal Coastlines, and Forest Fires and Percolation.
• ### Monte Carlo Estimation for Pi

This is the description and instructions for the Monte Carlo Estimation of Pi applet. It is a simulation of throwing darts at a figure of a circle inscribed in a square. It shows the relationship between the geometry of the figure and the statistical outcome of throwing the darts.
• ### **Can You Beat Randomness: The Lottery Game

This is the description and instructions for the Can You Beat Randomness?- The Lottery Game applet. It is a simulation of flipping coins. Students are asked to make conjectures about randomness and how certain strategies affect randomness. It strives to show the "growth of order out of randomness."
• ### The One-Dimensional Random Walk

This is the description and instructions for the One-Dimensional Random Walk applet. This Applet relates random coin-flipping to random motion. It strives to show that randomness (coin-flipping) leads to some sort of predictable outcome (the bell-shaped curve).
• ### The Two-Dimensional Random Walk

This is the description and instructions for the Two-Dimensional Random Walk applet. This Applet relates random coin-flipping to random motion but in more than one direction (dimension). It covers mean squared distance in the discussion.
• ### The Anthill and Molecular Motion

This is the description and instructions for the the Anthill and Molecular Motion applet. Topics include mixing, diffusion, and contour plots.
• ### Diffusion Limited Aggregation: Growing Fractal Structures

This site provides the description and instructions for as well as the link to the Diffusion Limited Aggregation: Growing Fractal Structures applet. This applet strives to describe, classify, and measure different random fractal patterns in nature.
• ### The Self-Avoiding Random Walk

This site provides the description and instructions for as well as the link to The Self-Avoiding Random Walk applet. In the SAW applet, random walks start on a square lattice and then are discarded as soon as they self-intersect. If a random walk survives after N steps, we compute the square of the distance from the origin, sum it up, and divide by the number of survivals. This variable is plotted on the vertical axis of the graph, which is plotted to the right of the field where random walks travel.