STAT 400
Examples for 02/16/2011
Spring 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
)
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?
1 week
⇒
λ
= 1.4.
P
(
X = 0
) =
!
0
4
.
1
4
.
1
0
e

⋅
≈
0.2466
.
b)
What is the probability that there will be exactly 3 accidents next week?
1 week
⇒
λ
= 1.4.
P
(
X = 3
) =
!
3
4
.
1
4
.
1
3
e

⋅
≈
0.1128
.
c)
What is the probability that there will be at most 2 accidents next week?
1 week
⇒
λ
= 1.4.
P
(
X
≤
2
) = P
(
X = 0
) + P
(
X = 1
) + P
(
X = 2
)
=
!
!
!
2
4
.
1
1
4
.
1
0
4
.
1
4
.
1
2
4
.
1
1
4
.
1
0
e
e
e



⋅
⋅
⋅
+
+
≈
0.2466 + 0.3452 + 0.2417 =
0.8335
.
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What is the probability that there will be at least 2 accidents during the next
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 Spring '08
 Kim
 Poisson Distribution, Probability, Probability theory, Binomial distribution, Poisson

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