Difference between revisions of "BinomialDist Command"
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;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]]. | ||
| − | : | + | :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> ] | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Boolean Cumulative> ] | ||
:Returns a bar graph of a Binomial distribution when ''Cumulative'' = false. | :Returns a bar graph of a Binomial distribution when ''Cumulative'' = false. | ||
:Returns a bar graph of a cumulative Binomial distribution when ''Cumulative'' = true. | :Returns a bar graph of a cumulative Binomial distribution when ''Cumulative'' = true. | ||
:First two parameters are same as above. | :First two parameters are same as above. | ||
| − | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value | + | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ] |
| − | :Let X be a Binomial random variable. | + | :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'' = false. | ||
:Returns P( X ≤ ''v'') when ''Cumulative'' = true. | :Returns P( X ≤ ''v'') when ''Cumulative'' = true. | ||
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==CAS Specific Syntax== | ==CAS Specific Syntax== | ||
In [[CAS View]] only one syntax is allowed: | In [[CAS View]] only one syntax is allowed: | ||
| − | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value | + | ;BinomialDist[ <Number of Trials>, <Probability of Success>, <Variable Value>, <Boolean Cumulative> ] |
| − | :Let X be a Binomial random variable. | + | :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'' = false. | ||
:Returns P( X ≤ ''v'') when ''Cumulative'' = true. | :Returns P( X ≤ ''v'') when ''Cumulative'' = true. | ||
Revision as of 09:43, 26 April 2013
- 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 bar 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.
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.
