Difference between revisions of "Normal Command"

Revision as of 08:11, 4 October 2013

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).

Normal[ <Mean>, <Standard Deviation>, <Variable Value> ]: Calculates the function \Phi \left(\frac{x- \mu}{\sigma} \right) where Φ is the cumulative distribution function for N(0,1) with mean μ and standard deviation σ.; Example:
Normal[2, 0.5, 1] yields \frac{-erf(2/\sqrt{2})+1}{2}.

@@ Line 9: / Line 9: @@
 ;Normal[ <Mean μ>, <Standard Deviation σ>, <Variable Value v> ]
-:Calculates the function ''Φ((x – μ) / σ)'' at ''v'' where ''Φ'' is the cumulative distribution function for ''N(0,1)'' with mean ''μ'' and standard deviation ''σ''.
+:Calculates the function <math>\Phi \left(\frac{x- \mu}{\sigma} \right) </math> 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).}}