Normal Distribution
For a
- density function
- and distribution function
The diagram of the density function f(x) is often called Gaussian curve, or bell shaped curve. The distribution function Φ(x) is designated as Gaussian error function, because, according to Gauss, this distribution is assumed for the random errors in astronomical observations.
Expected value μ and variance σ2 are entered. For μ=0 and σ=1 you receive the standardized normal distribution.
Example:
μ = 5 , σ = .75 x ƒ(x) Φ(x) ————— –————— —————– 2 0,00017844 0,00003167 2,33333333 0,00095649 0,00018859 2,66666666 0,00420802 0,00093192 2,99999999 0,01519465 0,00383038 3,33333332 0,04503153 0,01313415 3,66666665 0,10953585 0,03772017 3,99999998 0,21868009 0,09121120 4,33333331 0,35832381 0,18703139 4,66666664 0,48189843 0,32836063 4,99999997 0,53192304 0,49999998 5,3333333 0,48189845 0,67163934 5,66666663 0,35832383 0,81296859 5,99999996 0,21868012 0,90878878 6,33333329 0,10953586 0,96227982

See also:
Setting the graphicsWikipedia: Normal distribution