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Homework 4 (Chapter 5) Solutions
1. Suppose that I take a bus home from my office, and that every 5 minutes a bus arrives at SAC.
Because of variation in the time that I leave my office, I don’t always arrive at the bus stop at the
same time, so my waiting time X for the next bus is a continuous r.v.
≤
≤
=
.
.
0
5
0
5
1
)
(
w
o
x
x
f
(a) What is the probability of waiting between 1 to 3 minutes?
(b)
5
2
5
1
5
3
5
5
1
)
(
)
3
1
(
3
1
3
1
3
1
=

=
=
=
=
≤
≤
∫
∫
x
dx
dx
x
f
X
P
(c) Or
5
2
)
1
3
(
5
1
)
3
1
(
=

=
≤
≤
X
P
.
(d)
(e) What is the probability of waiting for at least 4 minutes?
(f)
5
1
5
4
1
5
5
1
)
4
(
5
4
5
4
=

=
=
=
≥
∫
x
dx
X
P
.
(g)
2. Time until failure (in years) for a circuit board:
≥
=

.
.
0
0
2
)
(
2
w
o
x
e
x
f
x
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View Full Document (a) What is the probability that a circuit board lasts for at least 1 year:
135
.
2
)
(
)
1
(
2
1
2
1
2
1
=
=

=
=
=

∞

∞

∞
∫
∫
e
e
dx
e
dx
x
f
X
P
x
x
.
(b) What is the probability that a circuit board’s lifetime is between 6 months and 2 years?
350
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This note was uploaded on 09/14/2011 for the course AMS 310 taught by Professor Mendell during the Summer '08 term at SUNY Stony Brook.
 Summer '08
 Mendell

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