Difference between revisions of "Pascal Command"

Latest revision as of 18:20, 27 March 2018

Pascal( <n>, <p> ): Returns a bar graph of a Pascal distribution.

The Pascal distribution models the number of failures before the nth success in repeated mutually independent Bernoulli trials, each with probability of success p.

Pascal( <n>, <p>, <Boolean Cumulative> ): Returns a bar graph of a Pascal distribution when Cumulative = false.; Returns a graph of a cumulative Pascal distribution when Cumulative = true.; First two parameters are same as above.

Pascal( <n>, <p>, <Variable Value>, <Boolean Cumulative> ): Let X be a Pascal random variable and v the variable value.; Returns P( X = v) when Cumulative = false.; Returns P( X ≤ v) when Cumulative = true.; First two parameters are same as above.; Note: This command also works in the CAS View.; Example:
If the number of independent Bernoulli trials that must be successful is n = 1, the probability of success in one trial is p = \frac{1}{6}, then the probability of 2 failures before the success is given by
Pascal(1, 1/6, 2, false) which yields 0.12 in the Algebra View and 25/216 in the CAS View.

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=4.0}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude> {{command|cas=true|probability}}
-{{command|probability}}
+;Pascal( <n>, &lt;p> )
-;Pascal[ <Number of Successes r>, <Probability of Success p> ]:
+: Returns a bar graph of a [[w:Negative binomial distribution|Pascal distribution]].
-: Returns a bar graph of a [http://mathworld.wolfram.com/NegativeBinomialDistribution.html Pascal distribution].
-:''Parameters:''
-::''Number of Successes'': number of independent Bernoulli trials that must be successful
-::''Probability of Success'': probability of success in one trial
-;Pascal[ <Number of Successes>, <Probability of Success>, <Boolean Cumulative> ]
+The Pascal distribution models the number of failures before the ''n''th success in repeated mutually independent Bernoulli trials, each with probability of success ''p''.
-: Returns a bar graph of a Pascal distribution when ''Cumulative'' = false.
-: Returns a bar graph of a cumulative Pascal distribution when ''Cumulative'' = true.
-: First two parameters are same as above.
-;Pascal[ <Number of Successes>, <Probability of Success>, <Variable Value v>, <Boolean Cumulative> ]
+;Pascal( <n>, &lt;p>, <Boolean Cumulative> )
-: Let X be a Pascal random variable.
+:Returns a bar graph of a Pascal distribution when ''Cumulative'' = false.
-: Returns P( X = ''v'') when ''Cumulative'' = false.
+:Returns a graph of a cumulative Pascal distribution when ''Cumulative'' = true.
-: Returns P( X ≤ ''v'') when ''Cumulative'' = true.
+:First two parameters are same as above.
-: First two parameters are same as above.
-==CAS Syntax==
+;Pascal( <n>, &lt;p>, <Variable Value>, <Boolean Cumulative> )
-In [[CAS View]] only one syntax is allowed:
+:Let X be a Pascal random variable and ''v'' the variable value.
-;Pascal[ <Number of Successes>, <Probability of Success>, <Variable Value v>, <Boolean Cumulative> ]:
+:Returns P( X = ''v'') when ''Cumulative'' = false.
-: Let X be a Pascal random variable.
+:Returns P( X ≤ ''v'') when ''Cumulative'' = true.
-: Returns P( X = ''v'') when ''Cumulative'' = false.
+:First two parameters are same as above.
-: Returns P( X ≤ ''v'') when ''Cumulative'' = true.
+:{{note|This command also works in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]].}}
+:{{example|1=<div>If the number of independent Bernoulli trials that must be successful is n = 1, the probability of success in one trial is p = <math>\frac{1}{6}</math>, then the probability of 2 failures before the success is given by</div> <code><nowiki> Pascal(1, 1/6, 2, false)</nowiki></code> which yields ''0.12'' in the [[File:Menu view algebra.svg|link=|16px]] [[Algebra View]] and ''25/216'' in the [[File:Menu view cas.svg|link=|16px]] [[CAS View]].}}

Difference between revisions of "Pascal Command"

Latest revision as of 18:20, 27 March 2018

Pascal

Command Categories (All commands)