Difference between revisions of "Manuals/calci/BERNOULLIDISTRIBUTED"
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*The <math>Probability</math> vaule is ranges from 0 to 1. | *The <math>Probability</math> vaule is ranges from 0 to 1. | ||
*The Bernoulli distribution is defined by:<math>f(x)=p^x(1-p)^{1-x} </math> for x={0,1}, where p is the probability that a particular event will occur. | *The Bernoulli distribution is defined by:<math>f(x)=p^x(1-p)^{1-x} </math> for x={0,1}, where p is the probability that a particular event will occur. | ||
− | *The probability mass function is :<math>f(k,p) = \begin{cases}p | + | *The probability mass function is : |
− | + | <math>f(k,p) = \begin{cases} p if & k=1\\ | |
− | + | (1-p) if & k=0. \\ | |
+ | \end{cases}</math> | ||
*This function will give the result as error when | *This function will give the result as error when | ||
− | 1. Any one of the argument is | + | 1. Any one of the argument is non numeric. |
2. The value of p<0 or p>1. | 2. The value of p<0 or p>1. | ||
+ | |||
+ | ==Examples== | ||
+ | #BERNOULLIDISTRIBUTED(5,0.5) = 0 0 0 0 1 | ||
+ | #BERNOULLIDISTRIBUTED(9,0.8) = 0 1 1 1 1 1 1 1 1 | ||
+ | #BERNOULLIDISTRIBUTED(4,0.87) = 1 1 1 0 | ||
+ | |||
+ | ==Related Videos== | ||
+ | |||
+ | {{#ev:youtube|v=O8vB1eInP_8|280|center|Bernoulli Distribution}} | ||
+ | |||
+ | ==See Also== | ||
+ | *[[Manuals/calci/BERNOULLI | BERNOULLI]] | ||
+ | *[[Manuals/calci/KURT | KURT]] | ||
+ | *[[Manuals/calci/MULTINOMIAL | MULTINOMIAL]] | ||
+ | |||
+ | ==References== | ||
+ | [http://mathworld.wolfram.com/BernoulliDistribution.html Bernoulli Distribution] | ||
+ | |||
+ | |||
+ | |||
+ | *[[Z_API_Functions | List of Main Z Functions]] | ||
+ | |||
+ | *[[ Z3 | Z3 home ]] |
Latest revision as of 16:00, 4 December 2018
BERNOULLIDISTRIBUTED (Numbers,Probability)
- is the number of variables.
- is the value range from 0 to 1.
Description
- This function gives the value of the Bernoulli distribution.
- It is a discrete probability distribution.
- Bernoulli distribution is the theoretical distribution of the number of successes in a finite set of independent trials with a constant probability of success.
- The Bernoulli distribution is simply BINOM(1,P).
- This distribution best describes all situations where a trial is made resulting in either success or failure, such as when tossing a coin, or when modeling the success or failure.
- In , represents the number of variables.
- is the probability value.
- The vaule is ranges from 0 to 1.
- The Bernoulli distribution is defined by: for x={0,1}, where p is the probability that a particular event will occur.
- The probability mass function is :
- This function will give the result as error when
1. Any one of the argument is non numeric. 2. The value of p<0 or p>1.
Examples
- BERNOULLIDISTRIBUTED(5,0.5) = 0 0 0 0 1
- BERNOULLIDISTRIBUTED(9,0.8) = 0 1 1 1 1 1 1 1 1
- BERNOULLIDISTRIBUTED(4,0.87) = 1 1 1 0
Related Videos
See Also
References