Manuals/calci/CRITBINOM

CRITBINOM(ts,ps,alpha)

• $ts$ is the number of independent trials.
• $ps$ is the probability of success in one trial.
• $alpha$ is the criterion value.

Description

• the smallest value in Cumulative Binomial Distribution probability result is the Critbinom.
• This function is the inverse of the Cumulative Binomial Distribution.
• For example, the Critbinom function could be used to find the smallest number of through the dice for which there is a 40% chance of at least 10 six's.
• In CRITBINOM(ts,ps,alpha), $ts$ is the number of independent trials that are to be done (if $ts$ value is in decimal then it is converted to an integer), 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 ps} is the probability of success in one trial and 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 alpha} is the criterion value of the Cumulative Binomial Distribution (must be between 0 and 1).
• This function gives the result as error when

1.Any one of the argument is non-numeric.
2.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 ts<0}
,or 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 ps<0}
 or 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 ps>1}

3.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 alpha<0}
 or 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 alpha>1}

Examples

1. CRITBINOM(5,0.6,0.4) = 3
2. CRITBINOM(8,0.1,0.25) = 1
3. CRITBINOM(20,0.75,0.65) = 16
4. CRITBINOM(20,1,1.5) = NAN
5. CRITBINOM(9.5,0.4,0.35) = 3
6. CRITBINOM(12,-0.25,0.3) = NAN

See Also

• BINOMDIST
• NEGBINOMDIST
• COMBIN
• FACT

References

Binomial Distribution