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Problem Set 4  Econometrics 120A
Due Friday Dec 3
1. The goal of this problem is to derive how to construct a conﬁdence interval for probabilities. Suppose
Y
has an unknown distribution. Then for some number
a
we want a conﬁdence interval for
P
(
Y
≤
a
).
(Hint: Throughout, note this problem is highly linked to that of conﬁdence intervals for proportions).
(a) Let
X
= 1 if
Y
≤
a
and
X
= 0 otherwise. How does
E
[
X
] relate to
P
(
Y
≤
a
)? How does
Var(
X
) relate to
P
(
Y
≤
a
)?
(b) Suppose you see a sample of
{
Y
i
}
out of which you can construct a sample of
{
X
i
}
. Given your
answer to a), what is a good estimator for
P
(
Y
≤
a
)?
(c) What is the variance of your estimator in b)? How can you estimate this variance using the
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Unformatted text preview: sample? (d) Is the distribution of your estimator in b) approximately normal? Why or why not? (e) Using b), c) and d), explain how you can construct a 1α conﬁdence interval for P ( Y ≤ a ) using your estimator in b). (f) Suppose you see a sample { Y i } = { , 1 , 4 , 3 , 2 } . Using your answer in e) construct a 95% conﬁdence interval for P ( Y ≤ 1). 2. Questions 86 (page 264), 810 (page 267), 826 (page 283), 830 (page 285). 1...
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This note was uploaded on 12/05/2010 for the course ECON 120A taught by Professor M.abajian during the Spring '10 term at San Diego.
 Spring '10
 M.Abajian
 Econometrics

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