Answer Set 1 - Fall 2008

# Answer Set 1 Fall - Econ 371 Problem Set#1 Answer Sheet 2.1 In this question you are asked to consider the random variable Y which denotes the

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but, using Table 2.2 and our formula for computing means, we have that E ( X ) = k X X i =1 p i x i = (0 . 30) · 0 + (0 . 70) · 1 = 0 . 7 Substituting this into (1) yields. E ( W ) = 3 + 6 E ( X ) = 3 + 6(0 . 7) = 7 . 2 (2) Similarly, E ( Y ) = k Y X i =1 p i x i = (0 . 22) · 0 + (0 . 78) · 1 = 0 . 78 , so that E ( V ) = 20 - 7 E ( Y ) = 20 - 7(0 . 78) = 14 . 54 . (3) b. In part b you are asked to compute the corresponding variances for W and V . Equation (2.13) in the text tells us that: σ 2 W = 6 2 · σ 2 X = 36 σ 2 X σ 2 V = ( - 7) 2 · σ 2 Y = 49 σ 2 Y Turning to our formulas for variances, however, we know that: V ar ( X ) = k X X i =1 p i ( x i - μ X ) 2 = (0 . 30) · (0 - 0 . 7) 2 + (0 . 70) · (1 - 0 . 7) 2 = (0 . 30) · (0 . 49) + (0 . 70) · (0 . 09) = 0 . 21 So that σ 2 W = 6 2 · σ 2 X = 36(0 . 21) = 7
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## This note was uploaded on 08/09/2009 for the course ECON 120B taught by Professor Jeon during the Spring '08 term at UCSD.

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Answer Set 1 Fall - Econ 371 Problem Set#1 Answer Sheet 2.1 In this question you are asked to consider the random variable Y which denotes the

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