CS 3341
(Dr. Baron)
AntiMidterm (SOLUTIONS)
Solve any 3 of the following 4 problems. Each problem worth 20 pts.
Time: 1 hour 15 minutes. This is an openbook, opennotes test. Calculators
are allowed.
1. The time, in minutes, it takes to reboot a certain system is a continuous variable
with the density
f
(
x
) =
(
C
(10

x
)
,
if 0
< x <
10
0
,
otherwise
(a) Compute
C
.
(b) Compute the probability that it takes more than 6 minutes to reboot the
system.
SOLUTION.
(
a
)
Z
f
(
x
)
dx
=
Z
10
0
C
(10

x
)
dx
=

C
(10

x
)
2
2
ﬂ
ﬂ
ﬂ
ﬂ
ﬂ
x
=10
x
=0
=

C
0

100
2
= 50
C
= 1
,
therefore,
C=0.02
.
(
b
)
P
{
X >
6
}
=
Z
10
6
f
(
x
)
dx
=
Z
10
6
0
.
02(10

x
)
dx
=

0
.
02
(10

x
)
2
2
ﬂ
ﬂ
ﬂ
ﬂ
ﬂ
x
=10
x
=6
=

0
.
02
0

16
2
=
0.16
2. Before the computer is assembled, its vital component (motherboard) goes through
a special inspection. Only 80% of components pass this inspection.
(a) What is the probability that at least 18 of the next 20 components pass in
spection?
(b) What is the probability that at least 180 of the next 200 components pass
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 Spring '08
 baron
 Normal Distribution, Poisson Distribution, Probability theory, Binomial distribution, necessary continuity correction

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