The lifetimes x and y of two batteries (in years) are distributed according to the following joint pdf: fx, y (x, y) = ( 8e −4x e −2y if x ≥ 0 and y ≥ 0 0 otherwise (a) compute the probability that both batteries last at least 2 years. (b) find the marginal pdfs fx(x) and fy (y). (c) compute e[xy ]. (d) what is p(x ≤ y 2 ), the probability that the first battery lasts at most half as long as the second? (e) are x and y independent? why or why not?