Suppose the joint pdf of lifetimes of a certain part and a spare is given by

f(x, y) = e^{-(x + y)}; 0 < x < inf, 0 < y < inf

and zero otherwise. Find each of the following:

(a) The marginal pdfs, f₁(x) and f₂(y).

(b) The joint CDF, F(x, y)

(c) P[X > 2].

(d) P[X < Y].

(e) P[X + Y > 2].

(f) Are X and Y independent?