Question

Let X1, X2, X3 denote a random sample of size 3 from a gamma distribution with alpha=7 and theta=5.

a) Find the moment generating function of Y=X1+X2+X3

b) How is Y distributed?

Answer 1

MGF for a gamma distribution is M(t) = 1/(1-theta*t)^alpha. So do you just plug in alpha and theta? But what about y=x1+x2+x3