Difference between revisions of "BinomialDist Command"
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− | <noinclude>{{Manual Page|version=5.0}}</noinclude> | + | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|probability}} |
− | {{command|cas=true|probability}} | ||
;BinomialDist[ <Number of Trials>, <Probability of Success> ] | ;BinomialDist[ <Number of Trials>, <Probability of Success> ] | ||
:Returns a bar graph of a [[w:Binomial distribution|Binomial distribution]]. | :Returns a bar graph of a [[w:Binomial distribution|Binomial distribution]]. | ||
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==CAS Specific Syntax== | ==CAS Specific Syntax== | ||
− | In | + | In [[File:Menu view cas.svg|link=|16px]] [[CAS View]] only one syntax is allowed: |
;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ] | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ] | ||
:Let X be a Binomial random variable and let v be the variable value. | :Let X be a Binomial random variable and let v be the variable value. | ||
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:Returns P( X ≤ ''v'') when ''Cumulative'' = true. | :Returns P( X ≤ ''v'') when ''Cumulative'' = true. | ||
:{{example| 1=<div>Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is <math>\frac{1}{10}</math>, hence the propability of transfering an arbitrary packet successfully is <math>\frac{9}{10}</math>. | :{{example| 1=<div>Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is <math>\frac{1}{10}</math>, hence the propability of transfering an arbitrary packet successfully is <math>\frac{9}{10}</math>. | ||
− | :*<code><nowiki>BinomialDist[3, 0.9, 0, false]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 0, false]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully. |
− | :*<code><nowiki>BinomialDist[3, 0.9, 1, false]</nowiki></code> yields ''<math>\frac{27}{1000}</math>'', the probability of exactly one of three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 1, false]</nowiki></code> yields ''<math>\frac{27}{1000}</math>'', the probability of exactly one of three packets being transferred successfully. |
− | :*<code><nowiki>BinomialDist[3, 0.9, 2, false]</nowiki></code> yields ''<math>\frac{243}{1000}</math>'', the probability of exactly two of three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 2, false]</nowiki></code> yields ''<math>\frac{243}{1000}</math>'', the probability of exactly two of three packets being transferred successfully. |
:*<code><nowiki>BinomialDist[3, 0.9, 3, false]</nowiki></code> yields ''<math>\frac{729}{1000}</math>'', the probability of all three packets being transferred successfully. | :*<code><nowiki>BinomialDist[3, 0.9, 3, false]</nowiki></code> yields ''<math>\frac{729}{1000}</math>'', the probability of all three packets being transferred successfully. | ||
− | :*<code><nowiki>BinomialDist[3, 0.9, 0, true]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 0, true]</nowiki></code> yields ''<math>\frac{1}{1000}</math>'', the probability of none of the three packets being transferred successfully. |
− | :*<code><nowiki>BinomialDist[3, 0.9, 1, true]</nowiki></code> yields ''<math>\frac{7}{250}</math>'', the probability of at most one of three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 1, true]</nowiki></code> yields ''<math>\frac{7}{250}</math>'', the probability of at most one of three packets being transferred successfully. |
− | :*<code><nowiki>BinomialDist[3, 0.9, 2, true]</nowiki></code> yields ''<math>\frac{271}{1000}</math>'', the probability of at most two of three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 2, true]</nowiki></code> yields ''<math>\frac{271}{1000}</math>'', the probability of at most two of three packets being transferred successfully. |
:*<code><nowiki>BinomialDist[3, 0.9, 3, true]</nowiki></code> yields ''1'', the probability of at most three of three packets being transferred successfully. | :*<code><nowiki>BinomialDist[3, 0.9, 3, true]</nowiki></code> yields ''1'', the probability of at most three of three packets being transferred successfully. | ||
− | :*<code><nowiki>BinomialDist[3, 0.9, 4, false]</nowiki></code> yields ''0'', the probability of exactly four of three packets being transferred successfully | + | :*<code><nowiki>BinomialDist[3, 0.9, 4, false]</nowiki></code> yields ''0'', the probability of exactly four of three packets being transferred successfully. |
:*<code><nowiki>BinomialDist[3, 0.9, 4, true]</nowiki></code> yields ''1'', the probability of at most four of three packets being transferred successfully.</div>}} | :*<code><nowiki>BinomialDist[3, 0.9, 4, true]</nowiki></code> yields ''1'', the probability of at most four of three packets being transferred successfully.</div>}} |
Revision as of 15:52, 30 October 2015
- BinomialDist[ <Number of Trials>, <Probability of Success> ]
- Returns a bar graph of a Binomial distribution.
- The parameter Number of Trials specifies the number of independent Bernoulli trials and the parameter Probability of Success specifies the probability of success in one trial.
- BinomialDist[ <Number of Trials>, <Probability of Success>, <Boolean Cumulative> ]
- Returns a bar graph of a Binomial distribution when Cumulative = false.
- Returns a graph of a cumulative Binomial distribution when Cumulative = true.
- First two parameters are same as above.
- BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ]
- Let X be a Binomial random variable and let v be 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: A simplified syntax is available to calculate P(u ≤ X ≤ v): e.g.
BinomialDist[10, 0.2, 1..3]
yields 0.77175, that is the same as BinomialDist[10, 0.2, {1, 2, 3}].
CAS Specific Syntax
In CAS View only one syntax is allowed:
- BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ]
- Let X be a Binomial random variable and let v be the variable value.
- Returns P( X = v) when Cumulative = false.
- Returns P( X ≤ v) when Cumulative = true.
- Example:Assume transfering three packets of data over a faulty line. The chance an arbitrary packet transfered over this line becomes corrupted is \frac{1}{10}, hence the propability of transfering an arbitrary packet successfully is \frac{9}{10}.
BinomialDist[3, 0.9, 0, false]
yields \frac{1}{1000}, the probability of none of the three packets being transferred successfully.BinomialDist[3, 0.9, 1, false]
yields \frac{27}{1000}, the probability of exactly one of three packets being transferred successfully.BinomialDist[3, 0.9, 2, false]
yields \frac{243}{1000}, the probability of exactly two of three packets being transferred successfully.BinomialDist[3, 0.9, 3, false]
yields \frac{729}{1000}, the probability of all three packets being transferred successfully.BinomialDist[3, 0.9, 0, true]
yields \frac{1}{1000}, the probability of none of the three packets being transferred successfully.BinomialDist[3, 0.9, 1, true]
yields \frac{7}{250}, the probability of at most one of three packets being transferred successfully.BinomialDist[3, 0.9, 2, true]
yields \frac{271}{1000}, the probability of at most two of three packets being transferred successfully.BinomialDist[3, 0.9, 3, true]
yields 1, the probability of at most three of three packets being transferred successfully.BinomialDist[3, 0.9, 4, false]
yields 0, the probability of exactly four of three packets being transferred successfully.BinomialDist[3, 0.9, 4, true]
yields 1, the probability of at most four of three packets being transferred successfully.