Suppose that X1, . . . , Xn form a random sample from the gamma distribution with parameters α and β, where α is unknown and β is known. Show that if n is large, the distribution of the M.L.E. of α will be approximately a normal distribution with mean α and variance
[Γ(α)]2/n{Γ(α)Γ''(α) − [Γ'(α)]2}.