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STAT 400
Exam 2 Practice Problems
1. Heidi and Alex have agreed to meet for lunch between noon (0:00 p.m.) and 1:00 p.m.
Denote Heidi’s arrival time by X, Alex’s by Y, and suppose X and Y are independent
with probability density functions
f
X
(
x
) =
(
3
x
2
0
≤
x
≤
1
0
otherwise
f
Y
(
y
) =
(
5
y
4
0
≤
y
≤
1
0
otherwise
(a) Write down the joint p.d.f. of (
X,Y
).
(b) Find the probability that Heidi arrives before Alex.
1
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that are checked is lost. Suppose that a frequentﬂying businesswoman will be checking
120 bags over the course of the next year. Using Poisson approximation to ﬁnd the
probability that she will lose 2 or more pieces of luggage.
3. Suppose that commercial airplane crashes in a certain country occur at the rate of 2.5
per year. Assume that such crashes follow a Poisson process,
(a) Starting from now, let
X
denotes the time until the next crash, what is the
distribution of
X
? Write down the p.d.f. of
X
.
(b) What is the probability that the next crash will occur within three months?
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 Spring '05
 TBA
 Statistics, Probability

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