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Show, using m.g.f.’s that if ?1~Exp(?), ?2~Exp(?) and ?1 ⊥ ?2 ,then (?1 + ?2 )~Gamma...

Show, using m.g.f.’s that if ?1~Exp(?), ?2~Exp(?) and ?1 ⊥ ?2 ,then (?1 + ?2 )~Gamma (2, 1/? ). You may assume that the m.g.f. of a Gamma(?, ?) random variable is 1 (1−??)^? ,? < 1 /?

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