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## Homework Statement

Let X denote a random variable with the following probability mass function:

P(j)= 2^(-j), j=1,2,3,.....

(a) Compute the moment generating function of X.

(b) Use your answer to part (a) to compute the expectation of X.

## Homework Equations

m.g.f of X is M (t) = E[e^tX]

## The Attempt at a Solution

I computed the MGF (X) to be: e^t/(2-e^t). I need a suggestion about the next step. I'm confused about the relationship between the MGF and expectation of X.

Thanks!