Let X1, …, Xn be a random sample from a gamma(α, β) population.
(a) Find the MLE of β, assuming α is known.
(b) If α and β are both unknown, there is no explicit formula for the MLEs of α and β, but the maximum can be found numerically. The result in part (a) can be used to reduce the problem to the maximization of a univariate function. Find the MLEs for α and β for the data in Exercise 7.10(c).