What is the Poisson Distribution? Dr. Ron Tibben-Lembke.

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Presentation transcript:

What is the Poisson Distribution? Dr. Ron Tibben-Lembke

Ce n'est pas les petits poissons. Les poissons How I love les poissons Love to chop And to serve little fish First I cut off their heads Then I pull out the bones Ah mais oui Ca c'est toujours delish Les poissons Hee hee hee Hah hah hah With the cleaver I hack them in two I pull out what's inside And I serve it up fried God, I love little fishes Don't you?

Simeon Denis Poisson "Researches on the probability of criminal and civil verdicts" 1837 looked at the form of the binomial distribution when the number of trials was large. He derived the cumulative Poisson distribution as the limiting case of the binomial when the chance of success tend to zero.

Binomial Distribution Given n trials P = probability of success each time X = number of successes in total Probability of x successes in n tries:

Poisson Distribution

POISSON(x,mean,cumulative) X is the number of events. Mean is the expected numeric value. Cumulative is a logical value that determines the form of the probability distribution returned. If cumulative is TRUE, POISSON returns the cumulative Poisson probability that the number of random events occurring will be between zero and x inclusive; if FALSE, it returns the Poisson probability mass function that the number of events occurring will be exactly x.