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Unformatted text preview: Final Practice Problems Answer Key 1. The following is a fictional joint probability distribution for level of education and income. Level of education is in the left most row and income on the top most row. Education/Income 20,000 50,000 90,000 High School 4 25 4 25 2 25 College 6 25 6 25 3 25 (a) What is the probability that income is 20,000? What is the probability that income is 50,000? What is the probability that income is 90,000? Let I denote income, E stand for education, H for High School and C for college. Then, P ( I = 20 , 000) = P ( I = 20 , 000; E = H ) + P ( I = 20 , 000; E = C ) = 10 / 25 Similarly, P ( I = 50 , 000) = 10 / 25 and P ( I = 90 , 000) = 5 / 25. (b) Conditional on a High School education what is the probability of having an income of 90,000? First note that arguing as in (a) we obtain P ( E = H ) = 10 / 25. Hence, P ( I = 90 , 000  E = H ) = P ( I = 90 , 000; E = H ) P ( E = H ) = 2 / 25 10 / 25 = 2 10 (c) Conditional on a College education what is the probability of having an income of 90,000? Since P ( E = C ) = 15 / 25 we obtain: P ( I = 90 , 000  E = C ) = 3 / 25 15 / 25 = 3 15 (d) Are level of education and income independent? To answer this question you need to check P ( E = a ; I = b ) = P ( E = a ) P ( I = b ) for a { H,C } and b { 20 , 000 , 50 , 000 , 90 , 000 } . Algebra verifies this is indeed the case and that education and income are independent. (e) A study argues that college graduates have higher incomes than people with only a high school degree. Do the numbers in the table support or contradict this claim? Fully justify your answer. Since education and income are independent they are not related to each other and in particular college graduates do not have higher incomes than high school graduates. 2. A researcher is trying to understand the expected level of income in the United States. Let X i be the level of income for person # i in his sample of 100 people....
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This note was uploaded on 11/30/2010 for the course ECON 120A 1684210 taught by Professor Elliot during the Spring '10 term at UCSD.
 Spring '10
 Elliot

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