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Unformatted text preview: Midterm Exam 2 Practice Problems Answer Key 1. A fictional study examined the joint distribution of education levels and GDP levels across countries. The following is the joint probability distribution. Education is entered in the left most column, and GDP in the top most row. Education/GDP Low Medium High Low 0.3 0.1 Medium 0.1 0.2 0.1 High 0.05 0.05 0.1 (a) What is the probability that a country has a High level of Education? What is the probability that it has Low level of Education? To answer this question we need to compute the marginal distributions. Use E for Education, G for GDP and L for Low, M for Medium and H for High. Then we find P ( G = H ) by: P ( E = H ) = P ( E = H,G = L )+ P ( E = H,G = M )+ P ( E = H,G = H ) = 0 . 05+0 . 05+0 . 1 = 0 . 2 Similarly, we can find P ( E = L ) by: P ( E = L ) = P ( E = L,G = L ) + P ( E = L,G = M ) + P ( E = L,G = H ) = 0 . 3 + 0 . 1 + 0 = 0 . 4 (b) Conditional on a country having a High GDP level, what is the probability it has High level of Education? To answer this question we first need to find P ( G = H ). We proceed as in (a), to find: P ( G = H ) = P ( G = H,E = L ) + P ( G = H,E = M ) + P ( G = H,E = H ) = 0 + 0 . 1 + 0 . 1 = 0 . 2 The conditional probability is given by P ( E = H  G = H ) = P ( E = H,G = H ) /P ( G = H ) = . 1 / . 2 = 1 / 2. (c) Are GDP and education levels independent? Justify your answer. They are not independent. From (a) we know P ( E = H ) = 0 . 2 and from (b), P ( G = H ) = 0 . 2. Therefore, P ( G = H,E = H ) = 0 . 1 6 = (0 . 2) 2 = P ( G = H ) P ( E = H )....
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 Spring '10
 Elliot
 Normal Distribution, Standard Deviation, Probability theory

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