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April 7th, 2017, 12:03 PM   #1
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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?
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April 7th, 2017, 05:49 PM   #2
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Special case? b=1/θ???
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