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Unformatted text preview: distribution does not have all of its moments, it certainly does not have a mgf. 1.1 Examples 1. If a d.r.v. X has M X ( t ) = ( pe t + 1 ± p ) n ; what is the pmf? 2. Does a distribution exist for which M X ( t ) = t= (1 ± t ) ; j t j < 1 ? If yes, &nd it. If no, prove it. 3. In each of the following cases verify the expression given for the moment generating function, and in each case use the mgf to calculate EX and V arX . (a) P ( X = x ) = e & & ± x x ! , M X ( t ) = e ± ( e t & 1) ; x = 0 ; 1 ; 2 ;::: ; ² > 0; (b) f X ( x ) = e & ( x & ± ) 2 = (2 ² 2 ) p 2 ²³ , M X ( t ) = e ´t + ³ 2 t 2 = 2 , ±1 < x < 1 ; ±1 < & < 1 ; ± > . 1...
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This note was uploaded on 01/07/2012 for the course ECON 6190 taught by Professor Hong during the Fall '07 term at Cornell.
 Fall '07
 HONG
 Econometrics

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