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.