Difference between revisions of "BinomialDist Command"
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:*<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 | + | :*<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 | + | :*<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 | + | :*<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 | + | :*<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 09:54, 10 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 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.
