3.4 Functions of random variables. Assume that the locations of an incident and a response unit are independently, uniformly distributed over a rectangle with dimensions X0, Y0 (see Exercise 3.1). The sides of the rectangle are defined parallel to directions of travel. If the incident and response unit locations are (X1, Y1) and (X2, Y2), respectively, the travel distance is

D = |X1 - X2| + |Y1 - Y2|

a. For the case X0 = Y0, find the pdf of D.

b. For the case X0 Y0, identify the different regions of integration in the X, Y sample space that yield different functional forms for the pdf of D.

c. (Optional) For the very brave, carry out the computations for part (b) to find the pdf of D when X0 > Y0.