I have the following moment generating function:
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
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?