Hi,

I have the following moment generating function:

$\displaystyle M_X(t) = 0.2e^{-3t}+0.11+0.1e^t+0.34e^{2t}+0.05e^{3t}+0.2e^{10t}$

I would like to find the support and the value of f_X(0) (i.e. the probability function of X evaluated at 0), but I am unsure how to go about doing this. I'm just guessing here, but couldn't X take on any value?

I also know that a moment generating function is defined as

$\displaystyle M_X(t) = \sum_{x \in X}e^{tx}f(x)$

So I factored e^t out of the original equation, but I'm not sure how to get the original equation into a summation in terms of x. Can someone help me understand this better?