I am doing some work with moment generating functions and have been given the question ''calculate the mean deviation'', this is defined to be E(lX-E(X)l).

My m.g.f is (1-t/lambda)^-1 and was generated from f(x)=(lambda)e^-(lambda)x.

I have no idea how to find MD from a m.g.f.

cheers

Here is a blunt approach:

Get from the mgf. Now use the pdf to calculate .

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Got by differentiating m.g.f once then setting t=0.

So do i manipulate the expectation of a random variable formula to look like:
= intergral |X - (1\lambda)| (lambda)e^-(lambda)x. dx?

Yes. And note that when and when .

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