Difference between revisions of "Normal Command"

Revision as of 11:02, 9 September 2015

Normal[ <Mean>, <Standard Deviation>, x ]: Creates probability density function (pdf) of normal distribution.

Normal[ <Mean>, <Standard Deviation>, x, <Boolean Cumulative> ]: If Cumulative is true, creates cumulative distribution function of normal distribution with mean μ and standard deviation σ, otherwise creates pdf of normal distribution.

Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]: Calculates the function \Phi \left(\frac{x- \mu}{\sigma} \right) at v where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.; Note: Returns the probability for a given x-coordinate's value (or area under the normal distribution curve to the left of the given x-coordinate).

Example:

Normal[2, 0.5, 1] yields 0.02 in the

Algebra View and \frac{erf(-\sqrt{2})+1}{2} in the

@@ Line 4: / Line 4: @@
 ;Normal[ <Mean>, <Standard Deviation>, x, <Boolean Cumulative> ]
-:If ''Cumulative'' is true, creates cumulative distribution function of normal distribution with mean ''μ'' and standard deviation ''σ'', otherwise creates pdf of normal distribution.
+:If ''Cumulative'' is true, creates cumulative distribution function of normal distribution with mean μ and standard deviation σ, otherwise creates pdf of normal distribution.
 ;Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]
@@ Line 10: / Line 10: @@
 :{{note| Returns the probability for a given ''x''-coordinate's value (or area under the normal distribution curve to the left of the given ''x''-coordinate).}}
-==CAS Syntax==
+:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields ''0.02'' in the [[File:Menu view algebra.svg|links=|16px]] [[Algebra View]] and <math>\frac{erf(-\sqrt{2})+1}{2}</math> in the [[File:Menu view cas.svg|links=|16px]] [[CAS View]].</div>}}
-;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ]
-:Calculates the function  <math>\Phi \left(\frac{x- \mu}{\sigma} \right) </math> where ''Φ'' is the cumulative distribution function for ''N(0,1)'' with mean ''μ'' and standard deviation ''σ''.
-:{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{erf(-\sqrt{2})+1}{2}</math>.</div>}}