STAT 400
Examples for 09/15/2011
Fall 2011
Poisson Distribution:
X
= the number of occurrences of a particular event in an interval of time or space.
P(
X
=
x
) =
!
λ
λ
x
x
e

⋅
,
x
= 0, 1, 2, 3, … .
E(
X
)
=
λ
,
Var(
X
)
=
λ
.
Table III
( pp. 580 – 582 )
gives
P(
X
≤
x
)
EXCEL:
=
POISSON(
x
,
λ
,
0
)
gives
P(
X
=
x
)
=
POISSON(
x
,
λ
,
1
)
gives
P(
X
≤
x
)
1.
Traffic accidents at a particular intersection follow Poisson distribution with
an average rate of 1.4 per week.
a)
What is the probability that the next week is accidentfree?
b)
What is the probability that there will be exactly 3 accidents next week?
c)
What is the probability that there will be at most 2 accidents next week?
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d)
What is the probability that there will be at least 2 accidents during the next
two weeks?
e)
What is the probability that there will be exactly 5 accidents during the next
four weeks?
f)
What is the probability that there will be 2 accidents tomorrow?
g)
What is the probability that the next accident will not occur for three days?
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 Fall '08
 Kim
 Statistics, Normal Distribution, Poisson Distribution, Probability, Probability theory, Poisson, Poisson random variable

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