. Suppose we have a miniload AS / RS system. Assume the rack is 20 meters long and 10 meters high. The horizontal spwd is 4 meters per second, and the vertical speed is 2 meters per second. Suppose that 25% of the items cause 90% of the activity and are stored in the quarter of the rack that is closest to the i ,f o point. Let T be the time from the i / o point (located in the lower left corner) to the retrieval location (X ,Y]. (a) Compute the joint p.d.f. of (X,Y]. (b) Compute the marginal p.d.f. X . (c) Compute the marginal p.d.f. Y. (d) Compute the conditional p.d.f. of Y given X = 5. (e) Compute the conditional p.d.f. of Y given X = 15. (f) Compute the expected value of Y given X = 5. (g) Compute the expected value of Y given X = 15. (h) Compute PT E 5 seconds. (i) Compute the c.d.f. of T