2. Suppose there is a miniload with a rack that has length 100 and height 50. The mast moves horizontally with speed 4 and vertically with speed 2. Assume the lower left corner of the rack is at the origin and that the s/r machine needs to go from the origin to a random location (X, Y). Assume that 80% of the activity is caused by 25% of the items, and the high turnover items are stored in the area of the rack that can be reached most quickly. Let T be the travel time from the origin to to (X, Y). (a) Compute F X,y(50, 25). (b) Determine the joint p.d.f. of (X, Y). (c) Compute the marginal p.d.f. of Y (d) Compute the conditional p.d.f. of Y given X = 25. (e) Compute E[Y | X = '75]. (f) Express the travel time T as a function of (X, Y). (g) Determine the c.d.f. of T