If X₁,X₂, . . . , X_n is a random sample from a distribution having pdf of the form f(x; θ) = θx^θ−1, 0 < x < 1, zero elsewhere, show that a best critical region for testing H₀ : θ = 1 against H₁ : θ = 2 is C = {(x₁, x₂, . . . , x_n) : c ≤ Пⁿ_i=1 x_i}.