Mid2Problems3A - Midterm Exam 2 Practice Problems Answer...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 )....
View Full Document

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.

Page1 / 3

Mid2Problems3A - Midterm Exam 2 Practice Problems Answer...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online