3.7 AVL systems. Suppose that the individual x and y errors of an AVL system are independently distributed according to a Laplace pdf,

Suppose that the radius of error is measured directly in terms of right-angle distance,

R = |X_{e}| + |Y_{e}|

Show that

f_{R}(r) = r^{2}e^{-r} where r 0

and thus

E[R] = 2/

[You might try obtaining (*) using both the "never-fail" method and the "infinitesimal method" outlined in Example 3.]