Transcription of The Poisson and Exponential Distributions
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The Poisson and Exponential Distributions
Published by theApplied probability Trust Applied probability Trust 2005123 The Poisson andExponential DistributionsJOHN C. B. COOPER1. IntroductionThe Poisson distribution is a discrete distribution with probability mass functionP(x)=e xx!,wherex=0,1,2,.., the mean of the distribution is denoted by , and e is the variance of this distribution is also equal to .The Exponential distribution is a continuous distribution with probability density functionf(t)= e t,wheret 0 and the parameter >0. The mean and standard deviation of this distributionare both equal to 1/ .The cumulative Exponential distribution isF(t)= 0 e tdt=1 e t.(1)2. Relation between the Poisson and Exponential distributionsAn interesting feature of these two Distributions is that, if the Poisson provides an appropriatedescription of the number of occurrences per interval of time, then the Exponential will providea description of the length of time between occurrences.
The Poisson distribution is a discrete distribution with probability mass function P(x)= e−µµx x!, where x = 0,1,2,..., the mean of the distribution is denoted by µ, and e is the exponential. The variance of this distribution is also equal to µ. The exponential distribution is a continuous distribution with probability density function f ...
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