If X has a Gamma distribution with parameters α and β, derive the moment generating function of X and use it to find the mean and variance of X. (b) (5points) An engineer determines that the oil loss claim size for a certain class of motor engines is a random variable with moment generating function mY​(t)=1/(1− 2500t)4, use mY​(t) to derive the standard deviation of the claim size for this class of engines.