Difference between revisions of "Manuals/calci/BINOMIALDISTRIBUTED"
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| − | <div style="font-size:30px">'''BINOMIALDISTRIBUTED (Numbers,Probability)'''</div><br/> | + | <div style="font-size:30px">'''BINOMIALDISTRIBUTED (Numbers,Probability,Trials)'''</div><br/> |
*<math>Numbers</math> is the number of variables. | *<math>Numbers</math> is the number of variables. | ||
*<math>Probability</math> is the value from 0 to 1. | *<math>Probability</math> is the value from 0 to 1. | ||
| + | *<math>Trials</math> is the any positive real number. | ||
==Description== | ==Description== | ||
*This function gives the value of the Binomial distribution. | *This function gives the value of the Binomial distribution. | ||
| − | *In <math>BINOMIALDISTRIBUTED (Numbers,Probability)</math>, <math>Numbers</math> is the number of the variables and <math>Probability</math> is the probability value which varies from 0 to 1. | + | *In <math>BINOMIALDISTRIBUTED (Numbers,Probability,Trials)</math>, <math>Numbers</math> is the number of the variables and <math>Probability</math> is the probability value which varies from 0 to 1.<math> Trial </math> is any positive real number. |
*This gives the discrete probability distribution. | *This gives the discrete probability distribution. | ||
*The probability of getting exactly k successes in n trials is given by the Probability Mass Function: | *The probability of getting exactly k successes in n trials is given by the Probability Mass Function: | ||
<math> b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math> for k=0,1,2,3...n where <math>\binom{n}{k}</math> is the COMBIN(n,k) i.e.<math> \binom{n}{k} = \frac{n!}{k!(n-k)}!</math> | <math> b(k;n,p)=Pr(X = k) = \binom{n}{k}p^{k}(1-p)^{n-k}</math> for k=0,1,2,3...n where <math>\binom{n}{k}</math> is the COMBIN(n,k) i.e.<math> \binom{n}{k} = \frac{n!}{k!(n-k)}!</math> | ||
| − | *The Cumulative Binomial Distribution is:<math>B(x;n,p) = Pr(X \le x) =\sum_{i=0}^x \binom{n}{i}p^{i}(1-p)^{(n-i)}</math> | + | *The Cumulative Binomial Distribution is:<math>B(x;n,p) = Pr(X \le x) =\sum_{i=0}^x \binom{n}{i}p^{i}(1-p)^{(n-i)}</math>. |
| + | |||
| + | ==Examples== | ||
| + | # BINOMIALDISTRIBUTED(10,0.4) = 36 42 45 41 41 38 37 36 32 41 | ||
| + | # BINOMIALDISTRIBUTED(5,0.3,76) = 23 29 20 19 23 | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|v=WWv0RUxDfbs|280|center|Binomial Distribution}} | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | *[[Manuals/calci/BINOMDIST | BINOMDIST]] | ||
| + | *[[Manuals/calci/COMBIN | COMBIN]] | ||
| + | *[[Manuals/calci/FACT | FACT]] | ||
| + | |||
| + | ==References== | ||
| + | [http://en.wikipedia.org/wiki/Binomial_distribution Binomial Distribution] | ||
| + | |||
| + | |||
| + | |||
| + | *[[Z_API_Functions | List of Main Z Functions]] | ||
| + | |||
| + | *[[ Z3 | Z3 home ]] | ||
Latest revision as of 17:59, 5 December 2018
BINOMIALDISTRIBUTED (Numbers,Probability,Trials)
- is the number of variables.
- is the value from 0 to 1.
- is the any positive real number.
is the number of variables.
is the value from 0 to 1.
is the any positive real number.Description
- This function gives the value of the Binomial distribution.
- In , is the number of the variables and is the probability value which varies from 0 to 1. is any positive real number.
- This gives the discrete probability distribution.
- The probability of getting exactly k successes in n trials is given by the Probability Mass Function:
, 
is any positive real number.for k=0,1,2,3...n where is the COMBIN(n,k) i.e.
for k=0,1,2,3...n where 
is the COMBIN(n,k) i.e.
- The Cumulative Binomial Distribution is:.
.Examples
- BINOMIALDISTRIBUTED(10,0.4) = 36 42 45 41 41 38 37 36 32 41
- BINOMIALDISTRIBUTED(5,0.3,76) = 23 29 20 19 23
Related Videos
See Also
References