1.3.6.6.19. Poisson Distribution | Poisson distribution mean
![1.3.6.6.19. Poisson Distribution](https://i.imgur.com/axBPWDg.jpg)
1.ExploratoryDataAnalysis[1]1.3.EDATechniques[2]1.3.6.ProbabilityDistributions[3]1.3.6.6.GalleryofDistributions[4]1.3.6.6.19.PoissonDistributionProbabilityMassFunction[5]ThePoissondistributionisusedtomodelthenumberofeventsoccurringwithinagiventimeinterval.TheformulaforthePoissonprobabilitymassfunctionis(p(x;lambda)=frac{e{-lambda}lambda{x}}{x!}mbox{for}x=0,1,2,cdots)λistheshapeparameterwhichindicatestheaveragenumberofeventsinthegiventimeinterval.ThefollowingistheplotofthePoissonprobabilityde...
![1.3.6.6.19. Poisson Distribution](https://i.imgur.com/H8YKUrg.jpg)
The formula for the Poisson probability mass function is
( p(x;lambda) = frac{e{-lambda}lambda{x}} {x!} mbox{ for } x = 0, 1, 2, cdots )
λ is the shape parameter which indicates the average number of events in the given time interval.
The following is the plot of the Poisson probability density function for four values of λ.
Cumulative Distribution Function [6] The formula for the Poisson cumulative probability function is
( F(x;lambda) = sum_{i=0}{x}{frac{e{-lambda}lambda{i}} {i!}} )
The following is the plot of the Poisson cumulative distribution function with the same values of λ as the pdf plo...