STAT 408
Spring 2009
Version A
Name
ANSWERS
.
Section __________
Quiz 4
(10 points)
Be sure to show all your work; your partial credit might depend on it.
No credit will be given without supporting work.
1.
Suppose that number of accidents at the Monstropolis power plant follows the Poisson
process with the average rate of 0.40 accidents per week.
Notations:
X
t
= number of accidents in
t
weeks.
T
k
= time of the
k
th accident.
a)
(3)
Find the probability that the first accident would occur during the fourth week.
T
1
has
Exponential
distribution with
λ
= 0.40
or
θ
=
1
/
0.4
= 2.5.
P
(
3 < T
1
< 4
)
=
∫

4
3
4
.
0
4
.
0
dt
t
e
=
e
–
1.2
–
e
–
1.6
≈
0.0993
.
OR
P
(
3 < T
1
< 4
)
=
P
(
T
1
> 3
)
– P
(
T
1
> 4
)
=
P
(
X
3
= 0
)
– P
(
X
4
= 0
)
=
P
(
Poisson
(
1.2
)
= 0
)
– P
(
Poisson
(
1.6
)
= 0
)
=
0.301 – 0.202
=
0.099
.
OR
k
fourth wee
the
during
accident
one
least
at
weeks
e
first thre
the
during
accidents
no
P
AND
=
P
(
X
3
= 0
)
×
P
(
X
1
≥
1
)
=
0.301
×
(
1 – 0.670
)
≈
0.0993
.
OR
Week 1
Week 2
Week 3
Week 4
no accident
no accident
no accident
accident(s)
0.670
×
0.670
×
0.670
×
0.330
≈
0.0993
.
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b)
(4)
Find the probability that the third accident would occur during the fifth week.
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 Spring '08
 STEPANOV
 Statistics, Poisson Distribution, Probability theory, Exponential distribution, Poisson process

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