3.9 Functions of random variables (derived distributions) Consider a square service region of unit area in which travel is right-angle and directions of travel are parallel to the sides of the square. Let (X₁, Y₁) be the location of a mobile unit and (X₂, Y₂) the location of a demand for service. The travel distance is

D = D_x + D_y

where

D_x = |X₁ - X₂| and D_y = |Y₁ - Y₂|

We assume that the two locations are independent and uniformly distributed over the square.