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Logistics and Transportation Planning Methods
Massachusetts Institute of Technology
Quiz 1
November 4, 2002
"Well, I'm countin' on a miracle”
 The “Boss” (Bruce Springsteen)
No miracles are needed; just answer all questions, showing all work.
This is an OPEN BOOK quiz.
Good luck.
Total time allotted is 85 minutes.
Please print your name clearly on each blue book you use.
Please begin each question (there are 2) in a new book.
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Problem #1.
50 points
(a) [25 points] Consider the square that is 1.0 km on a side shown in Figure 1.
Two points
X
1
and
X
2
are uniformly independently located on the perimeter of the square.
The location
X
1
represents a police car and
X
2
an emergency incident.
Travel can only occur on the perimeter
of the square.
That is, there are no roads internal to the square.
(i) Find the probability density function (pdf) for the travel distance between
X
1
and
X
2
, assuming the police car follows a shortest path on the perimeter of the square and
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 Fall '06
 hansman

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