Difference between revisions of "Pascal Command"
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| − | <noinclude>{{Manual Page|version= | + | <noinclude>{{Manual Page|version=5.0}}</noinclude> {{command|cas=true|probability}} |
| − | {{command|cas=true|probability}} | + | ;Pascal( <n>, <p> ) |
| − | ;Pascal | + | : Returns a bar graph of a [[w:Negative binomial distribution|Pascal distribution]]. |
| − | : Returns a bar graph of a [ | + | |
| − | + | 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''. | |
| − | + | ||
| − | + | ;Pascal( <n>, <p>, <Boolean Cumulative> ) | |
| − | ;Pascal | + | :Returns a bar graph of a Pascal distribution when ''Cumulative'' = false. |
| − | :Returns a bar graph of a Pascal distribution when ''Cumulative'' = false. | + | :Returns a graph of a cumulative Pascal distribution when ''Cumulative'' = true. |
| − | :Returns a | ||
:First two parameters are same as above. | :First two parameters are same as above. | ||
| − | ;Pascal | + | |
| − | :Let X be a Pascal random variable. | + | ;Pascal( <n>, <p>, <Variable Value>, <Boolean Cumulative> ) |
| − | :Returns P( X = ''v'') when ''Cumulative'' = false. | + | :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. | :Returns P( X ≤ ''v'') when ''Cumulative'' = true. | ||
:First two parameters are same as above. | :First two parameters are same as above. | ||
| − | + | :{{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]].}} | |
| − | : | ||
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| − | :{{example|1=<div> | ||
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.
