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The Poisson Distribution
•
The Poisson Distribution is another
extremely important distribution in
Probability and Statistics.
It is
especially important for Industrial
Engineers for reasons that will
become apparent.
•
The distribution was discovered by
SiméonDenis Poisson (1781–1840)
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Relation to Binomial
The Poisson distribution is derived from
the Binomial by letting N¸ 1 and p&0
but all the time keeping Np=&
constant.
For example:
N
10
100
1000
10,000

.......
&
= 1 always
1/5/10
Mean and Variance
•
The mean and variance of the
Poisson can be shown (after a lot of
tedious math) to be:
E(X) = &
and V(X) =
1
λ
=
=
=

=

=
=
=
∑
∑
∑
∑
∑
∞
=

∞
=


∞
=

∞
=

∞
=

)
1
(
!
)
(
!
)
1
(
!
)
1
(
!
!
)
(
0
1
1
1
1
0
k
k
j
j
j
j
j
j
j
j
k
e
j
e
j
e
j
je
j
je
X
E
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Example
Suppose 100 chips are manufactured
on a line which has historically
produced 5% defective chips.
What is
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This note was uploaded on 01/04/2010 for the course STATS 1100 taught by Professor Rodriguez during the Spring '08 term at Pittsburgh.
 Spring '08
 Rodriguez
 Statistics, Poisson Distribution, Probability

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