Econ140FinalFall2008

# Econ140FinalFall2008 - Econ 140 Department of Economics...

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Unformatted text preview: Econ 140 Department of Economics Fall 2008 Prof. Armando Levy FINAL EXAM You have 180 minutes to complete the exam. There are 6 questions worth 135 total points. The problems are not ranked by difficulty. Please write your answers on the exam itself and show all work. Good luck. 1. Suppose you are playing Craps in Las Vegas, and have just rolled an 8 on your first roll (thereby setting the point). To determine your passline bet you will continue to roll the pair of dice until you either duplicate your roll on 8 (and you win) or you roll a 7 (and lose). Let X be the random variable that is the number of rolls you will make after this first roll of 8 to determine the outcome. Assume the dice are fair and rolls are independent of each other. a. (5 points) What is the probability that X=1 ? b. (3 points) What is the probability that X&gt;1 ? c. (2 points) What is the probability that X=2 conditional on X&gt;1 ? d. (5 points) Sketch the cdf of X for X &lt;= 4 . Page 1 of 12 Econ 140 Department of Economics Fall 2008 Prof. Armando Levy 2. More on dice: Suppose we want to test whether a particular die is loadedi.e. not equally likely to show any of the six outcomes (you may remember this was an issue in Oceans 13). We roll the die n times and record the number of times we rolled 1, 2,..,6 denoted n 1 ,, n 6 . a. (5 points) One thing we could do is calculate the sample expectation of rolling k as n k/ n and test whether its significantly different than 1/6 at the 5% significance level. What is the test statistic you would construct? b. (5 points) What is the distribution under the Null Hypothesis? c. (5 points) Explain why it would be invalid to perform six of these tests, one for each of the possible outcomes from our experiment? d. (5 points) Describe a simple regression equation that you could specify to test whether the die shows 3 dots 1/6 th of the time as it should. Page 2 of 12 Econ 140 Department of Economics Fall 2008 Prof. Armando Levy 3. In this question, we will use regression models to try to identify and estimate sibling peer effects. Our data set consists of observations of schooling outcomes and individual characteristics for i = 1,,N households in Indonesia. Each of our households has two siblings. Y1 i denotes the test score of the oldest sibling, and Y2 i denotes the test score of the youngest sibling. Scores are recorded at the end of primary school. One would expect that a sibling's exam score might be affected by the other's score. There are many possible reasons for this, including: 1) siblings may work together and learn from one another, 2) younger siblings look up to older siblings and emulate their performance (good or bad in school), or 3) if your older sibling does well in school, you might try to distinguish yourself from your sibling and not do well in school, but do well in something else. Assume that we write down the following model for how sibling test scores are interrelated: Y 1 i = = 0 + 1...
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## Econ140FinalFall2008 - Econ 140 Department of Economics...

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