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) =...
Opengraph URL: https://mathworld.wolfram.com/PoissonDistribution.html
Domain: mathworld.wolfram.com
| DC.Title | Poisson Distribution |
| DC.Creator | Weisstein, Eric W. |
| DC.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) =... |
| DC.Date.Modified | 2008-11-23 |
| DC.Subject | 62E |
| DC.Rights | Copyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement. |
| DC.Format | text/html |
| DC.Identifier | https://mathworld.wolfram.com/PoissonDistribution.html |
| DC.Language | en |
| DC.Publisher | Wolfram Research, Inc. |
| DC.Relation.IsPartOf | https://mathworld.wolfram.com/ |
| DC.Type | Text |
| Last-Modified | 2008-11-23 |
| og:image | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_PoissonDistribution.png |
| og:type | website |
| twitter:card | summary_large_image |
| twitter:image:src | https://mathworld.wolfram.com/images/socialmedia/share/ogimage_PoissonDistribution.png |
| None | ie=edge |
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