Urban OR Quiz 1
October 20, 2003
“We blew it.”
Henry Fonda (Easy Rider)
Don’t blow it: Just answer all questions, showing all work. Good luck.
1. Suppose that x
1
and x
2
are independent and both U(0,a), and let G(a) be the
expected value of the
cube
of the larger of the two variables.
Use Crofton’s
method to determine G(a).
2.
Suppose that vehicles are distributed over a large city under a spatial Poisson
process with parameter
λ
, and let v
i
be the straightline distance to a given point
from the i
th
nearest vehicle to that point. Find the probability that v
4
> 4v
1
and
also that v
4
> 2v
2
. (We are referring to the joint event involving v
1
and v
2
, not
two separate events.)
3. Mendel arrives at a random time to ride the Lemon Line, on which the intervals
between trains are equally like to be 4, 5, and 6 minutes.
(i)
What is the probability that he waits between 4 and 5 minutes for the
next train? (HINT: What is the conditional probability that he waits
between 4 and 5 minutes if he arrives in an interval of length X?)
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 Fall '06
 hansman
 Probability theory, Exponential distribution, Repair Shop, ith nearest vehicle, Lemon Line

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