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Unformatted text preview: This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 120 APPENDIX C SOLUTIONS TO PROBLEMS C.1 (i) This is just a special case of what we covered in the text, with n = 4: E( Y ) = and Var( Y ) = 2 /4. (ii) E( W ) = E( Y 1 )/8 + E( Y 2 )/8 + E( Y 3 )/4 + E( Y 4 )/2 = [(1/8) + (1/8) + (1/4) + (1/2)] = (1 + 1 + 2 + 4)/8 = , which shows that W is unbiased. Because the Y i are independent, Var( W ) = Var( Y 1 )/64 + Var( Y 2 )/64 + Var( Y 3 )/16 + Var( Y 4 )/4 = 2 [(1/64) + (1/64) + (4/64) + (16/64)] = 2 (22/64) = 2 (11/32). (iii) Because 11/32 > 8/32 = 1/4, Var( W ) > Var( Y ) for any 2 > 0, so Y is preferred to W because each is unbiased. C.3 (i) E( W 1 ) = [( n 1)/ n ]E( Y ) = [( n 1)/ n ] , and so Bias( W 1 ) = [( n 1)/ n ] = / n ....
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This note was uploaded on 09/11/2011 for the course ECONOMICS eco375 taught by Professor Suzuki during the Spring '11 term at University of Toronto Toronto.
 Spring '11
 Suzuki
 Econometrics

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