1. [Marks: 3+4] Let X be Binomial point process in W = [-2, 4] x [0, 4] with k points. Let A1 = [0, 2] x [1, 4), and A2 = [-1,3] x [0, 4] (a) Derive the distribution of N1 = Nx(Aj) and N2 = Ny (W \\ A2), and the value of COV[NI, N2]. (b) For k = 20 run 1000 simulations of X in W, and draw an histogram of of values of N1, N2, and /1 + NV2 out of the simulation, and interpret that result in terms of the distribution of distributions of each of the random variables. (Attach the code used and the plot of the histogram)