The Gauss distribution site describes how naturally the Gaussian distribution appears by taking a sum of independent identically distributed random variables. It provides an applet that shows the histogram of N replications of the sum of n random variables from a uniform (0,1) distribution. It also can graph the density function of a Gaussian distribution, thus showing how well the Gaussian distribution approximates the distribution of the sum of n independent random variables.

Type of Material:

Simulation

Recommended Uses:

This applet could be used as a classroom demonstration tool or as an aid to student experimentation.

Technical Requirements:

The applet requires a Java-enabled browser.

Identify Major Learning Goals:

The material presents students with several topics of probability theory and statistics. It shows how the fluctuations of a sum of random variables can be estimated by a normal distribution using the central limit theorem. It also shows how simulations can be used to estimate a distribution.

Target Student Population:

High school students or college students in probability and/or statistics courses.

Prerequisite Knowledge or Skills:

Students should be familiar with basic ideas of probability theory, such as randomness and simulations.

Content Quality

Rating:

Strengths:

The site contains an accurate introduction to the Gaussian distribution and the central limit theorem, as well as a clear description of what the applet does. The animated presentation of the developing ?bell curve? gives the user a good understanding of the Central Limit Theorem as a limiting process as opposed to presenting it as a static result. Giving the user control over the number of random variables and replications further strengthens this understanding.

Concerns:

None

Potential Effectiveness as a Teaching Tool

Rating:

Strengths:

The applet is an effective tool to make students think about random phenomenon. Randomness cannot be explained without experimentation. The site provides an applet to let students get their hands on randomness. This is done in two ways. First, the applet shows how the central limit theorem can be used to approximate the distribution of the sum of n independent random variables. Second, the applet allows quick simulations of this process. Seeing the results of the Central Limit Theorem verified repeatedly will reinforce its validity.

Concerns:

It would be nice if users of the applet could choose distributions other than the uniform (0,1) distribution for the independent random variables to be summed. This would further reinforce the validity of the CLT.

Ease of Use for Both Students and Faculty

Rating:

Strengths:

The applet is very use to use. It does N simulations of the sum of n independent identically distributed random variables with a uniform distribution. It allows the user to choose the values of n and of N. The output is shown quickly and progressively. The applet has button linking to a description of the central limit theorem and of the applet. It also has a help button. This help button describes how to deal with the window containing the applet.

Concerns:

None.

Creative Commons:

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