Moment Generating Function of a gamma distribution.
Hello Math Forums, this is my first time posting here so I apologize for not knowing all the functions of the board, but I just have a stats question that I am a bit lost on.
I am supposed to find the moment generating function of a gamma distribution with parameters α,[SIZE=2]β. Then, obtain the first two moments and use them to find the expected value and variance.
I know that the mgf of a gamma distribution is:
But from there I'm not sure how to generate the first two moments or find the expected value or variance. I would greatly appreciate any help on this. Thank you.