Manuals/calci/BERNOULLIDISTRIBUTED

BERNOULLIDISTRIBUTED (Numbers,Probability)

• $Numbers$ is the number of variables.
• $Probability$ 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 $BERNOULLIDISTRIBUTED(Numbers,Probability)$ ,$Numbers$ represents the number of variables.
• $Probability$ is the probability value.
• The $Probability$ vaule is ranges from 0 to 1.
• The Bernoulli distribution is defined by:$f(x)=p^{x}(1-p)^{1-x}$ for x={0,1}, where p is the probability that a particular event will occur.
• The probability mass function is :

$f(k,p)={\begin{cases}pif&k=1\\(1-p)if&k=0.\\\end{cases}}$

• 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

1. BERNOULLIDISTRIBUTED(5,0.5) = 0 0 0 0 1
2. BERNOULLIDISTRIBUTED(9,0.8) = 0 1 1 1 1 1 1 1 1
3. BERNOULLIDISTRIBUTED(4,0.87) = 1 1 1 0

See Also

• BERNOULLI
• KURT
• MULTINOMIAL

References

Bernoulli Distribution

• List of Main Z Functions

• Z3 home