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Poisson Distribution
This is a distribution useful for modeling of the number of events occuring in an interval of space or time,
for example, the number of automobiles arriving at a toll booth during a 10minute period or the number of
weak points in a square meter of plastic sheeting. The expected number of events that occur in one period
or region is constant and is called the
rate
parameter and is usually denoted by
λ
. The requirements for a
Poisson distribution are that (a) no two events can occur
simultaneously
, (b) events occur independently
in diFerent intervals, and (c) that the expected number of events in each time interval remain constant.
The probability mass function of a Poisson random variable
X
is given by
p
(
x
) =
e

λ
λ
x
x
!
,
x
= 0
,
1
,
2
, . . .
where
p
(
x
) =
P
(
X
=
x
), that is the probability that there are exactly
x
occurrences of an event in a
speci±ed interval, given that the expected number of occurrences of the event in the interval is
λ
. ²or
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.
 Spring '11
 Zhou
 Poisson Distribution

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