For an ergodic semi-Markov process.

(a) Compute the rate at which the process makes a transition from i into j.

(b) Show that , , = 11.

(c) Show that the proportion of time that the process is in state i and headed for state j is P., n., /,, where n,, = SF.,(t) dt

(d) Show that the proportion of time that the state is i and will next be j within a time x is P F(x). where F, is the equilibrium distribution of F.,