John throws a dart at a circular target with a radius of r. Suppose that with respect to a system of coordinates with the origin at the center of the target, the point where the dart lands may be represented as a bivariate normal vector Y = r/4 X, where X is a standard normal vector. (In particular, this means that John may not hit the target at all.) Let Z be the distance the dart lands from the center. Show that E{Z²} = r²/8. Find the probability that John will hit the target. Find P(Z ≤ r/4). (The use of software is recommended).