Difference between revisions of "Normal Command"
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==CAS Syntax== | ==CAS Syntax== | ||
;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ] | ;Normal[ <Mean>, <Standard Deviation>, <Variable Value> ] | ||
| − | :Calculates the function | + | :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(2/\sqrt{2})+1}{2}</math>.</div>}} | :{{example| 1=<div><code><nowiki>Normal[2, 0.5, 1]</nowiki></code> yields <math>\frac{-erf(2/\sqrt{2})+1}{2}</math>.</div>}} | ||
Revision as of 10:41, 3 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 Φ((x – μ) / σ) 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).
CAS Syntax
- 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}.
