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intro-ects-tut-2009-2-questions

intro-ects-tut-2009-2-questions - Econometrics(ECON0701...

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Econometrics (ECON0701) School of Economics & Finance, University of Hong Kong First semester, 2009-2010 Tutorial Exercise 2 (Teaching week starting from 21 September): Please be well prepared to answer the following questions. (Note that the lecture venue has changed to P3, Chong Yuet Ming Building with immediate e ff ect.) Assignment 1: Hand in Q. 7 to the mailbox of your tutor (Angela Mak) by 5 pm, 29 September (Tuesday). Please give logical, concise and precise answers and show your steps clearly. Marks will be deducted for inadequacy as well as redundancy or irrelevancy. You should work independently and hand in your own answers. 1. Let X 1 , X 2 , . . . , X n be independent random variables that all have the same probability distribution, with mean μ and variance σ 2 . Let X = 1 n n X i =1 X i . (a) Show that E ¡ X ¢ = μ . (b) Show that var ( X 1 + X 2 2 ) = σ 2 2 . (c) What is var ( X 1 + X n + X 3 3 ) ? (d) What is var ( X ) ?. 2. Consider the following simple regression model: y i = β 0 + β 1 x i + ε i . (1) De fi ne b β 0 and b β 1
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