Consider a discrete random variable X with the probability mass function as:

x 2 4 6 8 10 16

P(x) 0.1 0.2 0.35 0.2 0.1 0.05

Find the moment generating function of X.

Do I set it up as this?

0.1e^2t + 0.2e^4t + 0.35e^6t + 0.2e^8t + 0.1e^10t + 0.05e^16t

If so, what do I do from there? I feel like I'm on the total wrong track here.