I need detailed explanations for these problems.

6.13 Solutions. Spatial Poisson processes 1. It is easy to check from the axioms that the combined process N (t) = 3(1) + G(t) is a Poisson process with intensity )3 + y. (a) The time S (respectively, T) until the arrival of the rst brown (respectively, grizzly) bear is exponentially distributed with parameter )3 (respectively, 1/), and these times are independent. Now, \\ 00 PS T =f '55 'V'd =~. (