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PiE
PiE
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You cannot "invert" an MGF. The way it's done for MGF's is to compute it, then look at an MGF table and see which one it "resembles" and then deduceReplace $t$ with $it$ in the pdf or pmf from that.

Another way is to utilize LaPlace transforms as they are MGF's as wellmoment generating function. Then, if you determine the use an inverse Fourier transform, then you have to invert it to get the densitydistribution.

You cannot "invert" an MGF. The way it's done for MGF's is to compute it, then look at an MGF table and see which one it "resembles" and then deduce the pdf or pmf from that.

Another way is to utilize LaPlace transforms as they are MGF's as well. Then, if you determine the transform, then you have to invert it to get the density.

Replace $t$ with $it$ in the moment generating function. Then use an inverse Fourier transform to get the distribution.

Source Link
PiE
PiE
  • 111
  • 5

You cannot "invert" an MGF. The way it's done for MGF's is to compute it, then look at an MGF table and see which one it "resembles" and then deduce the pdf or pmf from that.

Another way is to utilize LaPlace transforms as they are MGF's as well. Then, if you determine the transform, then you have to invert it to get the density.