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.
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.