My Math Forum Mgf of an exponential distribution

 April 7th, 2017, 11:03 AM #1 Newbie   Joined: Nov 2013 Posts: 29 Thanks: 1 Mgf of an exponential distribution I need to mgf of the exponential distribution for another problem. In my text it says the mgf of a gamma is Mx(t)=(1-bt)^(-a) and since the exponential is a special case of gamma with a=1 and b=θ, I figured that the mgf of an exponential would be Mx(t)=(1-θt)^(-1). However on wikipedia, it says Mx(t)=θ/(θ-t). I can't see how these two equations are the same thing and for them to both be the mgf they'd have to be because of the uniqueness of the mgf. I believe wikipedia but I'm confused about why my method of finding the mgf doesn't work. Could someone make sense of this?
 April 7th, 2017, 04:49 PM #2 Global Moderator   Joined: May 2007 Posts: 6,821 Thanks: 723 Special case? b=1/θ???

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