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Unformatted text preview: ( X i ) = 2 . (4) By the LLN, 1 n P n i =1 X 2 i converges to E X 2 i , which is 2 . 3. (1) E ( X ) = P x =0 ; 1 xp ( x ) = 0 (1 & ) + 1 = . (2) The loglikelihood is given by P n i =1 log p ( X i ; ) = P n i =1 [ X i log + (1 & X i ) log (1 & )] . Take the FOC with respect to : 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 ML = 1 n P n i =1 X i . (3) E 1 n P n i =1 X i = 1 n P n i =1 E ( X i ) = . (4) By the LLN, 1 n P n i =1 X i converges to E ( X i ) , which is . 2...
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 Spring '08
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 Macroeconomics

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