STAT330 Lecture 7: 330 Lecture 7

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Ecet"d t e gh h a mgf mdt defined for f cthin suppose x has let of 4 is myct cbtmx at f a xt b where ufo then the mff t c cfai ad. Ecetlaxtbs ctbecetaxy etbpycat at e th h t t thatfu. X pet021467 eatmz to e eat t eatt t er. Exp if xu gammacx b then puts u bef ccpt. Cog apex da ptszpotto a catdp var. Getting moments with taylorexpansion if he can obtain a taylor expansion for mct so lk7co7 k. Nb power series h o a l l. Ekta d pok teak k p ca h k rca k. K coefficient of ek in the maclaurin series. Findthe maclaurin series for mtt moments and determinethe of x. Uniqueness theorem for mgfs suppose the r. ir x has mgf mitts and the r v. Y has megof myces matt mylt for all. Then x andy follow the same distribution t e th b.

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