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Unformatted text preview: Econ 140 Department of Economics Fall 2008 Prof. Armando Levy FIRST MIDTERM EXAM You have 90 minutes to complete the exam. There are 100 total points on the exam. Write your answers on the exam itself and show all work. Good luck. 1. (20 points) The following table presents some information about the students of the UC Berkeley in the Fall of 2007: American (Y=1) Non-American (Y=0) Total Undergraduate (X=1) 68% 2% 70% Graduate (X=0) 24% 6% 30% Total 92% 8% 100% Based on this information: a. Compute E(Y) and interpret the resulting number. Answer : E(Y) = 1 x P(Y=1) + 0 x P(Y=0) = P(Y=1) = 92%. So 92% of the students are American. b. Calculate and interpret E(Y|X=1) and E(Y|X=0). Answer : E(Y|X=1) = 1 x P(Y=1|X=1) + 0 x P(Y=0|X=1) = P(Y=1|X=1) = % 97 97 . 70 68 ) 1 ( ) 1 , 1 ( = 2245 = = = = X P X Y P So 97% of the undergraduate students are American. E(Y|X=0) = 1 x P(Y=1|X=0) + 0 x P(Y=0|X=0) = P(Y=1|X=0) = % 80 80 . 30 24 ) ( ) , 1 ( = = = = = = X P X Y P So 80% of the graduate students are American. Econ 140 Department of Economics Fall 2008 Prof. Armando Levy c. A randomly selected student on campus reports that he is non-American. What is the probability that this is an undergraduate student? What is the probability that this is a graduate student? Answer : Probability of being undergraduate given non-American: % 25 8 2 ) ( ) , 1 ( ) | 1 ( 2245 = = = = = = = Y P Y X P Y X P Probability of being graduate given non-American: % 75 8 6 ) ( ) , ( ) | ( 2245 = = = = = = = Y P Y X P Y X P 2. (15 points) Consider two variables X and Y such that X~N(12,4) and Y~N(4,9). A third variable Z is defined as Z=3X + 2Y. a. If the correlation between X and Y is 0.5, what is the distribution of Z (including its mean and variance)?...
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This note was uploaded on 02/17/2010 for the course ECON 141 taught by Professor Staff during the Fall '08 term at University of California, Berkeley.
- Fall '08