Manuals/calci/BINOMIALDISTRIBUTED

BINOMIALDISTRIBUTED (Numbers,Probability,Trials)

• $Numbers$ is the number of variables.
• $Probability$ is the value from 0 to 1.
• $Trials$ is the any positive real number.

Description

• This function gives the value of the Binomial distribution.
• In $BINOMIALDISTRIBUTED(Numbers,Probability,Trials)$, $Numbers$ is the number of the variables and $Probability$ is the probability value which varies from 0 to 1.$Trial$ 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:

$b(k;n,p)=Pr(X=k)={\binom {n}{k}}p^{k}(1-p)^{n-k}$ for k=0,1,2,3...n where ${\binom {n}{k}}$ is the COMBIN(n,k) i.e.${\binom {n}{k}}={\frac {n!}{k!(n-k)}}!$

• The Cumulative Binomial Distribution is:$B(x;n,p)=Pr(X\leq x)=\sum _{i=0}^{x}{\binom {n}{i}}p^{i}(1-p)^{(n-i)}$.

Examples

1. BINOMIALDISTRIBUTED(10,0.4) = 36 42 45 41 41 38 37 36 32 41
2. BINOMIALDISTRIBUTED(5,0.3,76) = 23 29 20 19 23

See Also

• BINOMDIST
• COMBIN
• FACT

References

Binomial Distribution

• List of Main Z Functions

• Z3 home