12-42. Let {X1, . . . ,Xn} depict a set of sample random variables taken from the

(gamma) probability density function f (x; α0, θ) = 1

(α0)θα0 xα0−1 e−x/θ , x ≥ 0; α0, θ > 0. Determine the most powerful test of size α ofH0 : θ = θ0 versus H1 : θ = θ1, with θ1 > θ0.