Difference between revisions of "Normal distribution"
Jump to navigation
Jump to search
BRichtigen (talk | contribs) (adding pics) |
BRichtigen (talk | contribs) (standard normal distribution) |
||
| Line 18: | Line 18: | ||
where | where | ||
<math>\mu</math> is the [[mean]] and <math>\sigma^2</math> is the [[variance]]. | <math>\mu</math> is the [[mean]] and <math>\sigma^2</math> is the [[variance]]. | ||
| + | |||
| + | If <math>\mu=0</math> and <math>\sigma=1</math>, the distribution is called the ''standard normal distribution'', often denoted by <math>\phi</math>: | ||
| + | :<math> | ||
| + | \phi(x) = \frac{1}{\sqrt{2\pi}} | ||
| + | \exp(-\frac{1}{2} x^2). | ||
| + | </math> | ||
| + | |||
[[category:Probability and Statistics]] | [[category:Probability and Statistics]] | ||
Revision as of 21:59, December 11, 2008
|
|
The normal distribution is a key distribution in the field of probability. It is also known as the the Gaussian distribution, after mathematician Carl Gauss, and the bell curve. The normal probability density function (PDF) is
- <math>
f(x)=\frac{1}{\sqrt{2\pi\sigma^2}} \exp\left[-\frac{1}{2\sigma^2}\left(x-\mu\right)^2\right] </math> where <math>\mu</math> is the mean and <math>\sigma^2</math> is the variance.
If <math>\mu=0</math> and <math>\sigma=1</math>, the distribution is called the standard normal distribution, often denoted by <math>\phi</math>:
- <math>
\phi(x) = \frac{1}{\sqrt{2\pi}} \exp(-\frac{1}{2} x^2). </math>