A spatially-homogeneous two-dimensional Poisson process (also called a spatial Poisson process) is defined such that the number of arrivals in a region A C R' has the Poisson distribution with parameter A x area(A), and if A1, A2, ...; An are disjoint subsets of R', then NA,, NA2. ..., NA., are independent random variables. Cell phone calls that arise at any fixed time in a given large cell can be modeled as a spatially-homogenous two-dimensional Poisson process with intensity A. At the center of the cell there is a base station tower. Let R1 denote the distance between the base station and the nearest caller. (a) Find the PDF of R1- b) Let R2 denote the distance between the base station and the second nearest caller. Find the joint PDF of Ri and R2- (c) Let R denote the distance between the nearest and the second nearest caller. Find E[R-]. Hint: Draw a picture to find R as a function of my and ry then use the law of total expectation