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HW02 answers Econ140A Winter2014

HW02 answers Econ140A Winter2014 - Economics 140A Winter...

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Economics 140A Winter 2014 Stearns and Wright Answers to Homework 2 1. a) E( 𝑥𝑥 ) = 0.3 1 + 0.3 2 + 0.4 3 = 2.1 b) E( 𝑥𝑥 2 ) = 0.3 1 2 + 0.3 2 2 + 0.4 3 2 = 5.1 c) var( 𝑥𝑥 ) = E( 𝑥𝑥 2 ) E( 𝑥𝑥 ) 2 = 0.69 . 𝑠𝑠𝑠𝑠𝑠𝑠 𝑠𝑠𝑑𝑑𝑑𝑑 ( 𝑥𝑥 ) = var( 𝑋𝑋 ) = .8307. 2. a) The sample mean is 3+2+1 3 = 2 . The sample median is the value in the middle, 2.0. The sample variance is ( 3−2 ) 2 + ( 2−2 ) 2 + ( 1−2 ) 2 3−1 = 1. 3. Since the data is normal, so is the mean. Since the normal is a continuous distribution, the probability of getting exactly a given value is effectively zero. 4. a) var( 𝑌𝑌 ) = 0.6 2 𝜎𝜎 𝑥𝑥 2 var( 𝑍𝑍 ) = 0.3 2 𝜎𝜎 𝑥𝑥 2 < var( 𝑌𝑌 ) , since 0.3 2 < 0.6 2 b) cov( 𝑌𝑌 , 𝑍𝑍 ) = 0.6 × 0.3 𝜎𝜎 𝑥𝑥 2 cov( 𝑋𝑋 , 𝑍𝑍 ) = 0.3 𝜎𝜎 𝑥𝑥 2 cov( 𝑋𝑋 , 𝑌𝑌 ) = 0.6 𝜎𝜎 𝑥𝑥 2 c) 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ( 𝑌𝑌 , 𝑍𝑍 ) = cov ( 𝑌𝑌 , 𝑍𝑍 ) �var ( 𝑌𝑌 ) var ( 𝑍𝑍 ) = 0 . 6 × 0 . 3𝜎𝜎 𝑥𝑥 2 �0 . 6 2 𝜎𝜎 𝑥𝑥 2 × 0 . 3 2 𝜎𝜎 𝑥𝑥 2 = 1 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐 ( 𝑋𝑋 , 𝑍𝑍 ) = cov( 𝑋𝑋 , 𝑍𝑍 ) var( 𝑋𝑋 ) var( 𝑍𝑍 ) = 0.3 𝜎𝜎
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