Let Y₁ < Y₂ < · · · < Y_n be the order statistics of a random sample of size n from a distribution that has pdf f(x; θ) = (1/θ)e^−x/θ, 0 < x < ∞, 0 < θ < ∞, zero elsewhere. Show that the ratio R = nY₁ / Σⁿ₁ Y_i and its denominator (a complete sufficient statistic for θ) are independent. Use the result of the preceding exercise to determine E(R^k), k = 1, 2, 3, . . . .