Manuals/calci/poisson

POISSON(x,m,cu)

• 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 x} is the number of events.
• 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 m } is the mean
• 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 cu} is the logical value like TRUE or FALSE.

Description

• This function gives the value of the Poisson distribution.
• The Poisson distribution is a discrete probability distribution for the counts of events that occur randomly in a given interval of time.
• It is is used to model the number of events occurring within a given time interval.
• In 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 POISSON(x,m,cu), x } is the number of events in a given interval of time, 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 m } is the Average numeric value and $cu$ is the logical value.
• If it is TRUE, this function will give the cumulative Poisson probability with the number of random events between 0 and x(included).
• If it is FALSE,this function will give the Poisson probability mass function with the number of events occuring will be exactly x.
• The 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 POISSON } probability mass function 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 f(x,\lambda)=\frac{\lambda^x.e^{-\lambda}}{x!}} , x=0,1,2,...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 \lambda } is the shape parameter 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 \lambda} >0.e is the base of the natural logarithm (e=2.718282).
• The cumulative Poisson probability function 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 F(k,\lambda)=\sum_{k=0}^x \frac{e^{-\lambda} .\lambda^k}{k!}} .
• This function will return the result as error when

1.x or m is nonnumeric.
2.x<0 or m<0.

Examples

1. POISSON(6,2,TRUE)=0.995466194
2. POISSON(6,2,FALSE)=0.012029803
3. POISSON(10.2,7,TRUE)=0.901479206
4. POISSON(10.2,7,FALSE)=0.070983269
5. POISSON(6,0,TRUE)=1

See Also

• EXPONDIST