Let Y(1), Y(2), Y(3), Y(4), Y(5) denote the order statistics of a random sample of size 5 from a distribution

Question

Let Y(1), Y(2), Y(3), Y(4), Y(5) denote the order statistics of a random sample of size 5 from a distribution having p.d.f. f(y) = e^(-y), 0 < y < ∞, zero elsewhere. Show that Z1 = Y(2) and Z2 = Y(4) − Y(2) are independent. Hint: First find the joint p.d.f. of Y(2) and Y(4).