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 = Dx + Dy


Dx = |X1 - X2| and Dy = |Y1 - Y2|

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

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