test1ans-3u03-2011w

# test1ans-3u03-2011w - ECON 3U03 Test 1 Instructor Shintaro...

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Unformatted text preview: ECON 3U03: Test 1 Instructor: Shintaro Yamaguchi February 1, 2011 1. Covariance. (a) Cov ( X 1 , X 3 ) = 0, because of independence (5 marks). • If independence is not mentioned, 3 marks are deducted. (b) E ( ¯ X ) = E [( X 1 + X 2 + X 3 ) / 3 ] = { E ( X 1 )+ E ( X 2 )+ E ( X 3 ) } / 3 = μ (10 marks). • No partial credit. (c) Var ( ¯ X )= Var (( X 1 + X 2 + X 3 ) / 3 )=[ Var ( X 1 )+ Var ( X 2 )+ Var ( X 3 )] / 9 = σ 2 / 3 (10 marks). • If the answer is Var ( ¯ X ) = σ 2 , 3 marks are deducted. • The following answer is also acceptable. Var ( ¯ X ) = E [ ¯ X- E ( ¯ X )] 2 = [ E ( ¯ X )] 2- μ 2 . Because of independence, I have [ E ( ¯ X )] 2 = [ E ( X 2 1 )+ E ( X 2 2 )+ E ( X 2 3 )] / 9. Notice that E ( X 2 i ) = Var ( X i )+ E ( X i ) 2 = σ 2 + μ 2 for i = 1 , 2 , 3. Thus, Var ( ¯ X ) = ( σ 2 + μ 2 ) / 3- μ 2 = σ 2 / 3. 2. LSQE: Theory (a) ∑ ( y t- b 1- b 2 x t ) 2 (5 marks)....
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test1ans-3u03-2011w - ECON 3U03 Test 1 Instructor Shintaro...

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