HW02_Econ140A_2011Fall

HW02_Econ140A_2011Fall - Economics 140A Fall 2011 Professor...

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Economics 140A Fall 2011 Professor Startz Homework 2 You may find the lecture notes “Review of Statistics” and Chapter R of the text helpful. 1. The random variable x can only take three possible values: 1 with prob=0.3, 2 with prob=0.3 and 3 with prob=0.4. a. What is the expected value, E(x), of x? b. What is the expected value of ± , ²( ± ) ?. c. What is ³´µ( ) ? ¶·¸¹¸º»( ) ? 2. The summation operator is commonly used in econometrics, and this exercise asks you to work out some of its useful properties. You have two variables i x and i y , each with N observations. You are given N i i x N x 1 1 and N i i y N y 1 1 . a. Show that ( ¼ ½ ̅) ¾ ¼¿À Á  . b. Show that ( ¼ ½ ̅) ± ¾ ¼¿À Á ∑ ¼ ± ¾ ¼¿À ½ à ̅ ± . c. Show that ( ¼ ½ ̅) ¾ ¼¿À ¼ ½ Ä Å) Á ∑ ( ¼ ½ ̅) ¾ ¼¿À Ä ¼ . d. For constants a, b, c and d, show that ¼ ½ Ç ̅)(ÈÄ ¼ ½ ¸Ä Å) ¾ ¼¿À Á ÆÈ ∑ ¼ Ä ¼ ½ ¾ ¼¿À Ã(Ƹ É ÇÈ ½ Ǹ) ̅Ä Å 3. Suppose you are given a data sample of three independent observations drawn from the normal distribution. The three values happen to be *ÊËÌËÍ+Î For this question, show how you’re doing the calculations rather than use a computer. a. What is the sample mean? The sample median? The sample variance? 4.
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This note was uploaded on 12/26/2011 for the course ECON 140a taught by Professor Staff during the Fall '08 term at UCSB.

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HW02_Econ140A_2011Fall - Economics 140A Fall 2011 Professor...

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