a) Let X and Y be independent random variables with moment generating functions f(t) and g(t), respectively. Let Z=X+Y. Determine MZ(t), the moment generating function of Z, in terms of f(t) and g(t).
b) Let X and Y be independent random variables that are both geometric distributions with likelihood of success equal to p. Using the previous problem, determine the moment generating function MZ(t) of Z=X+Y.