Please see the problem in the attachment.

Let X be a gamma random variable with parameter a and [3. The PDF of X is given by fx(x) = where a > 0 and [3 > 0, and 13 a xale 0 e tdt is a normalization constant. Show that MGF of X is given by n) [3 Mx(s) = Find E(x) and Var(X) in terms of a and using the NIGF.