thesaurus.maths.org

A continuous distribution whose graph looks like a bell-shaped curve. The distribution is symmetric. The probability density function is

ϕ( x ) = 1 σ √ 2 π exp   −(x − μ) 2 2 σ2  

The mean is μ and the variance is σ² . This distribution is notated N ( μ, σ² ) . A variable with this distribution can take any finite value.
This distribution occurs very often in real-world sets of data, and it is often the limit to which the sum of a large number of random variables tends.
It has MGF

M( θ) = exp( μθ+ 1 2 σ2 θ2 ) .

The cumulative distribution function of an N(0,1) random variable is usually written Φ(x) .

Distibution of the sum of many independent random variables (central limit theorem).
Typical normal distributed variables are:

• sample mean
  
• measurement error
  

A continuous distribution whose graph looks like a bell-shaped curve.
The distribution is symmetric.
The probability density function is

ϕ( x ) = 1 √ 2 πσ2 exp   −(x − μ) 2 2 σ2  

The mean is μ and the variance is σ² . This distribution is notated N ( μ, σ² ) . A variable with this distribution can take any finite value.