# quiz2BS-f07 - ECON 506-M Quiz2-B, October 4, 2007 NAME: I....

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Unformatted text preview: ECON 506-M Quiz2-B, October 4, 2007 NAME: I. Let Y be a random variable distributed as following: Y P(Y) 1 a 2 b Assuming E (Y) = 1.5, find the values of a and b. (8 points) Here you have to solve a system of equations (2 equations and 2 unknowns, a and b). 5 . 5 . 5 . 1 2 1 5 . 1 ) ( 2 1 1 = = = +- = = + = + a b b b Y E b a b a For the rest of this question, assume a = 0.3 and b = 0.7. Find the variance .( 8 points) For the variance we need to get the first and second moments. 21 . 7 . 1 1 . 3 ) ( 1 . 3 2 * 7 . 1 * 3 . ) ( 7 . 1 2 * 7 . 1 * 3 . ) ( 2 2 2 2 =- = = + = = + = Y V Y E Y E Find E( Y 5 ) (6 points) 25 . 3 ) 2 / 5 ( * 7 . 5 * 3 . ) / 3 ( = + = Y E II. A politician believes that 40% of voters would strongly support a proposal he wishes to advance. Suppose that this belief is correct. 5 voters are approached at random. What is the probability that at least one of the five would strongly support the proposal? (6 points) In this case we need to use a binomial distribution, since n=5 is fixed. Suppose that we consider a success when a macroeconomist support the proposal (then p=prob of...
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## This note was uploaded on 04/14/2011 for the course ECON 506 taught by Professor Staff during the Fall '08 term at University of Illinois, Urbana Champaign.

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quiz2BS-f07 - ECON 506-M Quiz2-B, October 4, 2007 NAME: I....

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