# Thread: Reversing the moment generating function

1. ## Reversing the moment generating function

So this is my moment generating function

Now i need to find the PDF or CDF

So i think the moment genereting function needs to be divided by

But how do i do this in an algabraic way
This is what i got so far

And now i'm stuck

2. ## Re: Reversing the moment generating function

Note that the mgf of a random variable is defined by

and mathematically speaking it is a Laplace transform of the corresponding pmf/pdf. Now you are given the mgf, and want to find the corresponding pmf/pdf, so generally speaking you would like to do an inverse-Laplace transform. There are table for this for many common functional form.

However, your mgf is easy enough to recognize. Think about how do you calculate the mgf for a discrete distribution, say a Binomial distribution. Then you can match the corresponding probabilities and support points. Also note that the Laplace transform is unique so you will have a unique solution.

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