10.17 Using a software package, simulate a Poisson process on the plane suitable for the previous two problems. Use = 2. With the help

10.17 Using a software package, simulate a Poisson process on the plane suitable for the previous two problems. Use λ = 2. With the help of this simulation, answer the following questions:

a) Estimate the probability that the circle of radius 1 centered at the origin of the plane contains two events.

b) Estimate the probability in part

a) of the problem 10.15. Use varying values for the distance r (say r ∈ {0.25, 0.5, 1, 2, 3, 4}). Use as many repetitions as you like. Do you obtain values close to what you should get?

c) Do the same thing as in part

b) but for the distance R2 − R1, with the Ri’s defined in the problem 10.16.