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# PS4 - sample(d Is the distribution of your estimator in b...

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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)?
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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 1-α 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 8-6 (page 264), 8-10 (page 267), 8-26 (page 283), 8-30 (page 285). 1...
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