Unformatted text preview: ( X i ) = ± 2 . (4) By the LLN, 1 n P n i =1 X 2 i converges to E ³ X 2 i ´ , which is ± 2 . 3. (1) E ( X ) = P x =0 ; 1 xp ( x ) = 0 ± (1 & ³ ) + 1 ± ³ = ³ . (2) The loglikelihood is given by P n i =1 log p ( X i ;³ ) = P n i =1 [ X i log ³ + (1 & X i ) log (1 & ³ )] . Take the FOC with respect to ³ : 1 ± P n i =1 X i & 1 1 & ± P n i =1 (1 & X i ) = 0 . Therefore, 1 ± (1 & ± ) P n i =1 X i & n 1 & ± = 0 , and we have b ³ ML = 1 n P n i =1 X i . (3) E µ 1 n P n i =1 X i ¶ = 1 n P n i =1 E ( X i ) = ³ . (4) By the LLN, 1 n P n i =1 X i converges to E ( X i ) , which is ³ . 2...
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This note was uploaded on 04/04/2011 for the course ECON 401 taught by Professor Staff during the Spring '08 term at University of Washington.
 Spring '08
 Staff
 Macroeconomics

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