3.6 A VL systems. If the travel distance metric of the vehicles being located by an AVL system is right angle, the travel distance between the vehicle's estimated and true positions is |X_e| + |Y_e|. Here X_e and Y_e are zero mean, variance ², independent Gaussian random variables representing x- and y-location estimation error, respectively, as described in Exercise 3.2. Making the necessary isotropy assumption, argue that

E[|X_e| + |Y_e|] = (4/) (/2) = 2 (2/)

Thus, the expected value of a Gaussian random variable with variance ² which is truncated at zero is
E[|X_e|] = E[|Y_e|] = (2/).