Transcript Document

What is the Poisson
Distribution?
Dr. Ron Tibben-Lembke
Ce n'est pas les petits poissons.
Les 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 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
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"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
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Given n trials
P = probability of success each time
X = number of successes in total
Probability of x successes in n tries:
 n x
n x
b( x, n, p)    p (1  p)
 x
Poisson Distribution
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e 
POISSON
x!
x

e 
CUMPOISSON 
k!
k 0
x
k
POISSON(x,mean,cumulative)
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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.