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.

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.

This resource consists of a Java applet and expository text. The applet is a simulation of the fire process, an interacting particle system consisting of a rectangular lattice of "trees". At each discrete time unit, each tree is either on green, on fire, or burnt. A tree on fire at a given time can catch neighboring trees on fire at the next time unit. The probabilities of fire spread can be varied.

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.

This resource consists of a Java applet and expository text. The applet illustrates the Galton board in which a ball falls through a triangular array of pegs. Various combinatorial ideas are illustrated, including combinations, bit strings, and binomial coefficients.

This resource consists of a Java applet and expository text. The applet simulates a random sample from a gamma distribution, and computes standard point estimates of the shape and scale parameters. The bias and mean square error are also computed.

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.

In this performance task, students consider two scenarios in a card game and conduct an experiment to analyze and compare experimental to theoretical probabilities with different game rules. In doing so, students will calculate probabilities to explore the effect of independent vs. dependent events on the outcomes in the card game.

Key concepts include:
a) conditional probability;
b) dependent and independent events;
c) mutually exclusive events;
d) counting techniques (permutations and combinations); and
e) Law of Large Numbers.

This resource consists of a Java applet and expository text. The applet allows the user to construct a histogram by clicking on a number line to generate the sample data. The class width can be varied and various summary statistics can be displayed.

This resource consists of a Java applet and expository text. The applet allows the user to construct a scatterplot by clicking on a graph to generate the bivariate data. The means, standard deviations, correlation, and the regression line are shown.

The microscopic world is full of phenomena very different from what we see in everyday life. Some of those phenomena can only be explained using quantum mechanics. This activity introduces basic quantum mechanics concepts about electrons that are essential to understanding modern and future technology, especially nanotechnology. Start by exploring probability distribution, then discover the behavior of electrons with a series of simulations.

Biology students often struggle to understand how it can be that the same two parents will produce genetically different offspring. This lab exercise is a very visual way to demonstrate the "making of a monster" one gene at a time. The resources include a full sheet of vocabulary and instructions, plus a data table to record the crosses. For advanced students, you can take the activity further with a sheet of follow up questions.

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.

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.

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.

Video Description:  What are citizen scientists? Why is their work so important to NASA? Join Dr. Michelle Thaller as she explains how the general public, using scientific protocols, careful observations and accurate measurements, can help NASA make exciting new discoveries. Find out how you can be a citizen scientist today.  Video Length:  4:26.NASA eClipsTM is a suite of online student-centered, standards-based resources that support instruction by increasing STEM literacy in formal and nonformal settings.  These free digital and downloadable resources inform and engage students through NASA-inspired, real-world connections.NASA eClips Real World segments (grades 6-8) connect classroom mathematics to 21st Century careers and innovations.  They are designed for students to develop an appreciation for mathematics through real-world problem solving.

 NASA eClips Real World:  The Carbon Cycle - Essential for Life on EarthVideo Description:  Carbon is an essential building block for life. Learning how carbon is converted through slow- and fast-moving cycles helps us understand how this life-sustaining element moves through the environment. Discover how NASA measures carbon through both field work and satellite imagery keeping watch through its eyes on the sky, on Earth, and in space.  This video won and Emmy Award in 2020.  Video Length:  5:43.NASA eClipsTM is a suite of online student-centered, standards-based resources that support instruction by increasing STEM literacy in formal and nonformal settings.  These free digital and downloadable resources inform and engage students through NASA-inspired, real-world connections.NASA eClips Real World segments (grades 6-8) connect classroom mathematics to 21st Century careers and innovations.  They are designed for students to develop an appreciation for mathematics through real-world problem solving.  

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.

This resource consists of a Java applet and expository text. The applet simulates a random sample from a normal distribution, and computes standard point estimates of the distribution mean and standard deviation. The bias and mean square error are also computed.

This resource consists of a Java applet and expository text. The applet simulates the order statistics of a random sample from a given distribution. The sample size, order, and sampling distribution can be specified.