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Title: Poisson Distribution -- from Wolfram MathWorld

Open Graph Title: Poisson Distribution -- from Wolfram MathWorld

X Title: Poisson Distribution -- from Wolfram MathWorld

Description: Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). (1) Viewing the distribution as a function of the expected number of successes nu=Np (2) instead of the sample size N for fixed p, equation (2) then becomes P_(nu/N)(n|N)=(N!)/(n!(N-n)!)(nu/N)^n(1-nu/N)^(N-n), (3) Letting the sample size N become large, the distribution then approaches P_nu(n) =...

Open Graph Description: Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). (1) Viewing the distribution as a function of the expected number of successes nu=Np (2) instead of the sample size N for fixed p, equation (2) then becomes P_(nu/N)(n|N)=(N!)/(n!(N-n)!)(nu/N)^n(1-nu/N)^(N-n), (3) Letting the sample size N become large, the distribution then approaches P_nu(n) =...

X Description: Given a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). (1) Viewing the distribution as a function of the expected number of successes nu=Np (2) instead of the sample size N for fixed p, equation (2) then becomes P_(nu/N)(n|N)=(N!)/(n!(N-n)!)(nu/N)^n(1-nu/N)^(N-n), (3) Letting the sample size N become large, the distribution then approaches P_nu(n) =...

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DC.TitlePoisson Distribution
DC.CreatorWeisstein, Eric W.
DC.DescriptionGiven a Poisson process, the probability of obtaining exactly n successes in N trials is given by the limit of a binomial distribution P_p(n|N)=(N!)/(n!(N-n)!)p^n(1-p)^(N-n). (1) Viewing the distribution as a function of the expected number of successes nu=Np (2) instead of the sample size N for fixed p, equation (2) then becomes P_(nu/N)(n|N)=(N!)/(n!(N-n)!)(nu/N)^n(1-nu/N)^(N-n), (3) Letting the sample size N become large, the distribution then approaches P_nu(n) =...
DC.Date.Modified2008-11-23
DC.Subject62E
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/PoissonDistribution.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
Last-Modified2008-11-23
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