Difference between revisions of "BinomialDist Command"
From GeoGebra Manual
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: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. | ||
| + | :{{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 beeing transfered successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 1, false]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of exactly one of three packets beeing transferd successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 2, false]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of exactly two of three packets beeing transferd successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 3, false]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of all three packets beeing transferd 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 beeing transfered successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 1, true]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of exactly one of three packets beeing transferd successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 2, true]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of exactly two of three packets beeing transferd successfully, | ||
| + | :*<code><nowiki>BinomialDist[3, 0.9, 3, true]</nowiki></code> yields <math>\frac{1}{1000}</math>, the probability of all three packets beeing transferd successfully. | ||
| + | |||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 1, false]</nowiki></code> yields <math>\frac{16}{45}</math>, the probability of selecting one white ball, | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 2, false]</nowiki></code> yields <math>\frac{1}{45}</math>, the probability of selecting both white balls, | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 3, false]</nowiki></code> yields ''0'', the probability of selecting three white balls. | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 0, true]</nowiki></code> yields <math>\frac{28}{45}</math>, the probability of selecting zero (or less) white balls, | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 1, true]</nowiki></code> yields <math>\frac{44}{45}</math>, the probability of selecting one or less white balls, | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 2, true]</nowiki></code> yields ''1'', the probability of selecting tow or less white balls and | ||
| + | :*<code><nowiki>BinomialDist[10, 2, 2, 3, true]</nowiki></code> yields ''1'', the probability of selecting three or less white balls.</div>}} | ||
Revision as of 14:18, 6 September 2011
- BinomialDist[ <Number of Trials>, <Probability of Success> ]
- Returns a bar graph of a Binomial distribution.
- Parameters:
- Number of Trials: number of independent Bernoulli trials
- Probability of Success: 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 v>, <Boolean Cumulative> ]
- Let X be a Binomial random variable.
- 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 v>, <Boolean Cumulative> ]
- Let X be a Binomial random variable.
- 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 beeing transfered successfully,BinomialDist[3, 0.9, 1, false]yields \frac{1}{1000}, the probability of exactly one of three packets beeing transferd successfully,BinomialDist[3, 0.9, 2, false]yields \frac{1}{1000}, the probability of exactly two of three packets beeing transferd successfully,BinomialDist[3, 0.9, 3, false]yields \frac{1}{1000}, the probability of all three packets beeing transferd successfully.BinomialDist[3, 0.9, 0, true]yields \frac{1}{1000}, the probability of none of the three packets beeing transfered successfully,BinomialDist[3, 0.9, 1, true]yields \frac{1}{1000}, the probability of exactly one of three packets beeing transferd successfully,BinomialDist[3, 0.9, 2, true]yields \frac{1}{1000}, the probability of exactly two of three packets beeing transferd successfully,BinomialDist[3, 0.9, 3, true]yields \frac{1}{1000}, the probability of all three packets beeing transferd successfully.
BinomialDist[10, 2, 2, 1, false]yields \frac{16}{45}, the probability of selecting one white ball,BinomialDist[10, 2, 2, 2, false]yields \frac{1}{45}, the probability of selecting both white balls,BinomialDist[10, 2, 2, 3, false]yields 0, the probability of selecting three white balls.BinomialDist[10, 2, 2, 0, true]yields \frac{28}{45}, the probability of selecting zero (or less) white balls,BinomialDist[10, 2, 2, 1, true]yields \frac{44}{45}, the probability of selecting one or less white balls,BinomialDist[10, 2, 2, 2, true]yields 1, the probability of selecting tow or less white balls andBinomialDist[10, 2, 2, 3, true]yields 1, the probability of selecting three or less white balls.
