NTNUJAVA Virtual Physics Laboratory
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Easy Java Simulations (2001- ) => modern physics => Topic started by: ahmedelshfie on May 05, 2010, 07:09:31 pm

Title: Gaussian distribution
Post by: ahmedelshfie on May 05, 2010, 07:09:31 pm
This applet created by prof Hwang
Modified by Ahmed
Original project Gaussian distribution (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=202.0)

Each coins in the applet can be up or down (represented by red or blue dots)
The applet simulate 100 coins were throwed each time and total number of coin in the up state will be added to the diagram.
The distribution become gaussian distrbution as the number of run increase to large value!

Title: Re: Gaussian distribution
Post by: ahmedelshfie on June 29, 2010, 08:33:02 pm
In probability theory and statistics, the normal distribution, or Gaussian distribution, is an absolutely continuous probability distribution with zero cumulants of all orders above two. The graph of the associated probability density function is “bell”-shaped, with peak at the mean, and is known as the Gaussian function or bell curve:

    $f(x) = \tfrac{1}{\sqrt{2\pi\sigma^2}}\; e^{ -\frac{(x-\mu)^2}{2\sigma^2} }$,

where parameters μ and σ 2 are the mean and the variance. The distribution with μ = 0 and σ 2 = 1 is called standard normal.

The normal distribution is often used to describe, at least approximately, any variable that tends to cluster around the mean. For example, the heights of adult males in the United States are roughly normally distributed, with a mean of about 70 inches (1.8 m). Most men have a height close to the mean, though a small number of outliers have a height significantly above or below the mean. A histogram of male heights will appear similar to a bell curve, with the correspondence becoming closer if more data are used.

By the central limit theorem, under certain conditions the sum of a number of random variables with finite means and variances approaches a normal distribution as the number of variables increases. For this reason, the normal distribution is commonly encountered in practice, and is used throughout statistics, natural sciences, and social sciences as a simple model for complex phenomena. For example, the observational error in an experiment is usually assumed to follow a normal distribution, and the propagation of uncertainty is computed using this assumption.

The Gaussian distribution was named after Carl Friedrich Gauss, who introduced it in 1809 as a way of rationalizing the method of least squares. One year later Laplace proved the first version of the central limit theorem, demonstrating that the normal distribution occurs as a limit of arithmetic means of any random variables. For this reason the normal distribution is sometimes called Laplacian, especially in French-speaking countries.
Data from  http://en.wikipedia.org/wiki/Normal_distribution