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Poisson and Normal Distributions

Poisson and Normal DistributionsLectures 7 Spring 2002 Poisson distribution The Poisson distribution can be derived as a limiting form ofthe binomial distribution in whichnis increased without limit asthe product =npis kept constant. This corresponds to conducting a very large number of Bernoullitrials with the probabilitypof success on any one trial being verysmall. The Poisson distribution can also be derived directly in a mannerthat shows how it can be used as a model of real situations. Inthis sense, it stands alone and is independent of the binomialdistribution.* Sim eon D. Poisson , (1781-1840).Lecture 71 Conceptual ModelImagine that you are able to observe the arrival of photons at adetector. Your detector is designed to count the number of photonsthat arrive in an interval .The Poisson distribution is based on three basic assumptions, listedon the next generality of the assumptions permits the model to be used inanalyzing many kinds of 72 Poisson Assumptions1.

Poisson Distribution • The Poisson∗ distribution can be derived as a limiting form of the binomial distribution in which n is increased without limit as the product λ =np is kept constant. • This corresponds to conducting a very large number of Bernoulli trials with the probability p of success on any one trial being very small. • The Poisson distribution can also be derived …

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