Discrete Geometric Moment Generating Function
I have a question regarding how to proceed with the following problem. I am required to produce a moment generating function for the following problem. I would like to know if the operation I performed is valid for this question. I never understood mgf's that well.
A balanced coin is flipped repeatedly until a head appears. Let X denote the number of flips needed. Define Y = 2X-1.
Find the moment generating function for Y.
This is a geometric distribution (discrete random variable).
I applied the definition of the m.g.f.
Note: I'm new to latex. Please consider the (2X-1) as raised to the power of e, along with the t.
Is this the valid first step for this problem, and others like it?
Thanks for your time!