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 , ( ) ?. c. What is ( ) ? ( ) ? 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 ( ̅) . b. Show that ( ̅) ̅ . c. Show that ( ̅) ( ̅) ∑ ( ̅) . d. For constants a, b, c and d, show that ( ̅)( ̅) ( ) ̅ ̅ 3. Suppose you are given a data sample of three independent observations drawn from the normal distribution. The three values happen to be * + 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. Suppose you drew three numbers from a normal distribution with mean 2.1. If you were to do this repeatedly, what fraction of the time would you expect the sample mean to be exactly 2.1? (The answer is never, but give a sentence or two of intuition as to why.)

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