normal random variable
When and , it is usually called standard normal distribution.
Cumulative distribution function
The cumulative distribution function of a standard normal variable, often denoted by
cannot be calculated in closed form in terms of the elementary functions, but its values are tabulated in most statistics books and here (http://planetmath.org/TableOfProbabilitiesOfStandardNormalDistribution), and can be computed using most computer statistical packages and spreadsheets.
Uses of the Gaussian distribution
The normal distribution is probably the most frequently used distribution. Its graph looks like a bell-shaped function, which is why it is often called bell distribution.
The normal distribution is important in probability theory and statistics. Empircally, many observed distributions, such as of people’s heights, test scores, experimental errors, are found to be more or less to be Gaussian. And theoretically, the normal distribution arises as a limiting distribution of averages of large numbers of samples, justified by the central limit theorem.
Relations to other distributions
The square of the standard normal random variable is the chi-squared random variable of degree 1. Therefore, the sum of squares of independent standard normal random variables is the chi-squared random variable of degree .
|Title||normal random variable|
|Date of creation||2013-03-22 11:54:20|
|Last modified on||2013-03-22 11:54:20|
|Last modified by||Koro (127)|
|Synonym||standard normal distribution|