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 |