s07pre1 - Prof. G. Jakubson Economics 321 Spring 2007...

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Prof. G. Jakubson Economics 321 March 2007 Spring 2007 PRELIMINARY EXAM #1 This is a closed book exam. You are permitted to have a calculator. There is a formula sheet at the end of the exam (Appendix 2), and some results that you will need to refer to in Appendix 1. Answer the questions below in an exam book or books. SHOW YOUR WORK ! Be sure to label each answer, and each part of each answer, clearly. Neatness counts -- if I cannot read it I cannot give you credit. Note that questions have different weights, and parts within a question may not be weighted equally. If you get stuck on a particular problem, skip it and move on to the next one. If you cannot remember exactly how to answer a question, you may get partial credit for setting it up even if you don't solve it. Read the questions carefully. Do Parts I (q1-5) and II (q6-7) in separate bluebooks. You have 75 minutes to complete the seven (7) questions on the exam. Part I (Questions 1-5) Do Parts I (q1-5) and II (q6-7) in separate bluebooks. 1. (15 points) In 1993, the distribution of infant mortality rates (deaths per 1000 lives births) over 131 countries with available data was as follow: Infant mortality Number of countries rate 0 to < 10 24 10 to < 20 24 20 to < 30 14 30 to < 50 18 50 to < 75 18 75 to < 100 16 100 to < 140 13 140 to 180 4 a. What is the median infant mortality rate within this group of countries? What assumption does this calculation of the median rely upon? b. Give the cumulative relative frequency distribution of infant mortality rates. (Use fractions rather than decimals to save time.) c. EXTRA CREDIT: Give the expressions that you would evaluate to find the mean infant mortality rate and the variance of infant mortality rates from these grouped data. (Do not evaluate them, but write down these expressions as functions of the available data.) 2. (30 points) Suppose you have data on a variable X. A "standardized" variable Z is constructed by using the following linear transformation: Z( XX ) / s ii =− x for each observation i = 1, . .., n. a. What is Z ? Economics 321, Applied Econometrics Page 1 of 6 Preliminary Exam #1, Spring 2007 c:\. ..\s07pre1.doc
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Economics 321, Applied Econometrics Page 2 of 6 Preliminary Exam #1, Spring 2007 c:\. ..\s07pre1.doc Part I (Questions 1-5) Do Parts I (q1-5) and II (q6-7) in separate bluebooks. b. What is s Z ? Now suppose that you measure a linear transformation of X, namely Y i = d 1 + d 2 X i for some values of d 1 and d 2 , and you construct a standardized measure of Y using T( YY ) / s ii =− Y . c. What are T and s T ? d. EXTRA CREDIT: The variance of a function of X, say g(X), is approximately (g') 2 s x 2 where g' is the first derivative. Let g(X) = e X , calculate its approximate variance, evaluate that variance at the mean of X.
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This note was uploaded on 05/26/2008 for the course ECON 3210 taught by Professor Molinari during the Spring '07 term at Cornell University (Engineering School).

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s07pre1 - Prof. G. Jakubson Economics 321 Spring 2007...

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