Shocks occur according to a Poisson process with intensity A, and each shock independently causes a certain system to fail with probability p. Let T denote the time at which the system fails and let N denote the number of shocks that it takes. (a) (2 points) Find the distribution of N. (b) (2 points) Find the distribution of T. (c) (2 points) Find the conditional distribution of N, given that T = t. (d) (2 points) Find the conditional distribution of T, given that N = n