Assume a sample i.i.d {9.4, 3.1, 4.4, 9.7, 22.8, 14.0, 5.6} measured in months over the lifetime of an artificial flavor. It is taken from a population whose density is f(x; β) = (e^(-x/β)) / (Γ(1)β) for x > 0 and zero elsewhere. Knowing that β > 0:
(a) Find the maximum likelihood estimator and the method of moments estimator for β.
(b) Give the estimated value β', so specify f(x; β).