HW1A - i X i Y i ( X i-X ) ( Y i-Y ) ( X i-X )( Y i-Y ) ( X...

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Econ 444 Elementary Econometrics (Winter 2010) ANSWERS TO HOMEWORK EXERCISE: 1 1. 1) A 2) B 2. (2.a) (2.b) E(X)=5.8333 and Var(X)= 4.3056. (2.c) Using properties of expected value E (2 + 3 X ) = 2 + 3 E ( X ) = 2 + 17 . 4999 = 19 . 4999 (19 . 5 approx). Similarly from properties of variance V ar (3 X ) = 9 × V ar ( X ) = 9 × 4 . 3056 = 38 . 7504. 3. (3.a) 6 i =1 X i Y i = X 1 Y 1 + X 2 Y 2 + X 3 Y 3 + X 4 Y 4 + X 5 Y 5 + X 6 Y 6 1
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(3.b) 4 i =1 X i Y i 4 i =1 X i 4 i =1 Y i = X 1 Y 1 + X 2 Y 2 + X 3 Y 3 + X 4 Y 4 ( X 1 + X 2 + X 3 + X 4 )( Y 1 + Y 2 + Y 3 + Y 4 ) 4. Calculations for this question are summarized below :
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Unformatted text preview: i X i Y i ( X i-X ) ( Y i-Y ) ( X i-X )( Y i-Y ) ( X i-X ) 2 1 9 21-3.33 7.34-24.4422 11.0889 2 12 16-0.33 2.34-0.7722 0.1089 3 16 4 3.67-9.66-35.4522 13.4689 Sum 37 41 0.01 0.02-60.6666 24.6667 (4.a) X = 12 . 33, and Y = 13 . 66. (4.b) 3 i =1 ( X i- X ) 2 = 24 . 66 (4.c) 3 i =1 ( X i- X )( Y i- Y ) =-60 . 66 2...
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HW1A - i X i Y i ( X i-X ) ( Y i-Y ) ( X i-X )( Y i-Y ) ( X...

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