10.15 A two-dimensional Poisson process is a general Poisson process with ???? =

R2, similar to the process presented in Example 10.3. More specifically, for any region of the plane A, the number of events in A, N(A), is a Poisson random variable with mean λ|A|, where |A| denotes the area of the region A. Furthermore, the events in any nonoverlapping region are independent. Consider the origin (0, 0) of the plane, and let X denote the Euclidian distance between the nearest event and the origin. Show that