Manuals/calci/BINOMIALDISTRIBUTED

BINOMIALDISTRIBUTED (Numbers,Probability)

• $Numbers$ is the number of variables.
• $Probability$ is the value from 0 to 1.

Description

• This function gives the value of the Binomial distribution.
• In $BINOMIALDISTRIBUTED(Numbers,Probability)$, $Numbers$ is the number of the variables and $Probability$ is the probability value which varies from 0 to 1.
• This gives the discrete probability distribution.
• The probability of getting exactly k successes in n trials is given by the Probability Mass Function:

$b(k;n,p)=Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}$ for k=0,1,2,3...n where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \binom{n}{k}} is the COMBIN(n,k) i.e.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \binom{n}{k} = \frac{n!}{k!(n-k)}!}

• The Cumulative Binomial Distribution is:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B(x;n,p) = Pr(X \le x) =\sum_{i=0}^x \binom{n}{i}p^{i}(1-p)^{(n-i)}} .

Examples

1. BINOMIALDISTRIBUTED(10,0.4) = 36 42 45 41 41 38 37 36 32 41

See Also

• BINOMDIST
• COMBIN
• FACT

References

Binomial Distribution

• List of Main Z Functions

• Z3 home