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( ? ) = 0.3 1 + 0.3 2 + 0.4 3 = 2.1 b) E( ? 2 ) = 0.3 1 2 + 0.3 2 2 + 0.4 3 2 = 5.1 c) var( ? ) = E( ? 2 ) E( ? ) 2 = 0.69 . ±²³ ³´µ ( ? ) = var( ) = .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 ) ¸ + ( 1·2 ) ¸ 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( ¹ ) = 0.6 2 º » 2 var( ¼ ) = 0.3 2 º » 2 < var( ¹ ) , since 0.3 2 < 0.6 2 b) cov( ¹ , ¼ ) = 0.6 × 0.3 º » 2 cov( , ¼ ) = 0.3 º » 2 cov( , ¹ ) = 0.6 º » 2 c) ½¾¿¿ ( ¹ , ¼ ) = cov ( À , Á ) var ( À ) var ( Á ) = 0 . 6 × 0 . à ¸ Ä0 . 6 ¸  à ¸ × 0 . 3 ¸  à ¸ = 1 ½¾¿¿ ( , ¼ ) = cov( , ¼ ) var( ) var( ¼ ) = 0.3 º » 2 º » 2 × 0.3 2 º » 2 = 1 ½¾¿¿ ( , ¹ ) = cov( ¹ , ) var( ¹ ) var( ) = 0.6 º » 2 0.6 2 º » 2 × º » 2 = 1 In general, any two variables that are linear functions of a third random variable are perfectly correlated.
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HW02 answers Econ140A Winter2014 - Economics 140A Winter...

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