60. A two-dimensional Poisson process is a process of randomly occurring events in the plane such that

(i) for any region of area A the number of events in that region has a Poisson distribution with mean ëÁ and

(ii) the number of events in nonoverlapping regions are independent.

For such a process consider an arbitrary point in the plane and let X denote its distance from its nearest event (where distance is measured in the usual Euclidean manner). Show that

(a) P{X> t] = e~X7rt2

(b> Em . ± .