Bivariate Normal Experiment
This resource consists of a Java applet and expository text. The applet simulates the bivariate normal distribution. The means are set at 0, but the standard deviations and the correlation can be varied. Simulated points from the distribution are shown as dots in a scatterplot.
Two-Type Poisson Experiment
This resource consists of a Java applet and expository text. The applet illustrates the arrivals in a Poisson process where each arrival, independently, is one of two types. The time interval, the rate of the process, and the probability that an arrival is type 1 can be varied. The applet illustrates "splitting" a Poisson process.
Red and Black Game
This resource consists of a Java applet and expository text. The applet allows the student to play the game of red and black, by betting on a sequence of Bernoulli trials until either a target is reached or the player is ruined. The target, initial fortune, and trial win probability can be varied.
Red and Black Experiment
This resource consists of a Java applet and expository text. The applet simulates the red and black experiment in which a player bets on a sequence of Bernoulli trials until a target fortune is reached or the player is ruined. The initial fortune, target fortune, and trial win probability can be varied, and the user can select either of two basic strategies: timid play or bold play.
Poisson Experiment
This resource consists of a Java applet and expository text. The applet simulates the arrivals in a Poisson process during a time interval. The length of the interval and the rate of the process can be varied. The applet illustrates the Poisson distribution and a special case of the central limit theorem.
Gamma Experiment
This resource consists of a Java applet and expository text. The applet simulates the time of the k'th arrival in a Poisson process. The arrival number k and the rate of the Poisson process can be varied. The applet illustrates the gamma distribution and a special case of the central limit theorem.
Triangle Experiment
This resource consists of a Java applet and expository text. The applet illustrates the triangle experiment: A stick is broken randomly into three parts. The events of interest are that the pieces form an acute triangle, an obtuse triangle, or no triangle.
Spinner Experiment
This resource consists of a Java applet and expository text. The applet simulates a basic spinner. The number of sectors and the probability of each sector can be specified.
Roulette Experiment
This resource consists of a Java applet and expository text. The applet is a simulation of the standard casino roulette game. The random variables of interest are the winning under various bets.
Random Walk Experiment
This resource consists of a Java applet and descriptive text. The applet illustrates a random walk on a discrete time interval from 0 to n. The time n and the probability of a step to the right can be varied. The random variables of interest are the final position, the maximum position, and the time of the last zero.
Problem of Points Experiment
This resource consists of a Java applet and descriptive text. The applet illustrates the problem of points: a coin is tossed until either n heads occurs or m tails occurs. The parameters n, m, and the probability of heads can be varied.
Poker Experiment
This resource consists of a Java applet and expository text. The applet simulates the basic poker experiment of dealing 5 cards from a standard deck. The random variable of interest is the type of hand.
Poker Dice Experiment
This resource consists of a Java applet and expository text. The experiment consists of rolling 5 fair dice. The random variable of interest is the type of hand.
Negative Binomial Experiment
This resource consists of a Java applet and descriptive text. The applet illustrates the number of trials needed to get a specified number of successes in Bernoulli trials, in terms of random points on a discrete timeline. The applet illustrates the negative binomial distribution. The number of successes and the probability of success can be varied.
Monty Hall Game
This resource consists of a Java applet and expository text. The applet consists of the Monty Hall game: a car is behind one door and goats are behind the other two doors. The player makes an initial choice and the host opens a different door. The player is then given the option of switching to the remaining door. The stochastic behavior of the host can be specified.
Monty Hall Experiment
This resource consists of a Java applet and expository text. The applet is a simulation of the Monty Hall experiment: a car is behind one door, goats are behind the other two doors. The player chooses a door and then the host opens another door. The player is given the option of switching to the remaining door. The stochastic behavior of the host and the probability of the player switching can be specified.
Matching Experiment
This resource consists of a Java applet and expository text. The applet is a simulation of the matching experiment, which consists of a random permutation of the first n positive integers. The random variable of interest is the number of matches (the number of integers in the random permutation that are in their correct positions). The applet illustrates the distribution of the number of matches and the convergence to the Poisson distribution.
Galton Board Experiment
This resource consists of a Java applet and descriptive text. The applet illustrates Bernoulli trials in terms of a Galton Board. The number of trials and the probability of success can be varied. The random variables of interest are the number of successes and the probability of a success. The applet illustrates the binomial distribution, the law of large numbers and the central limit theorem.
Finite Order Statistic Experiment
This resource consists of a Java applet and expository text. The applet is a simulation of the experiment of selecting n objects at random from the first m positive integers. The random variables of interest are the order statistics. The applet illustrates the distributions of the order statistics.
Die Coin Experiment
This resource consists of a Java applet and expository text. The applet simulates the experiment of rolling a die and then tossing a coin the number of times shown on the die. The die distribution and the probability of heads can be specified. The applet illustrates a two-stage experiment.
