Consider a Birth and Death process at {0, 1, 2, . . .} with p(0, 1) = p, p(0, 0) = 1p, p(i, i+ 1) = p, p(i, i 1) = q e p(i, i) = r for all i 1. Also consider that r > 0 and q > p

(a) Show that the chain is irreducible, aperiodic and positive recurrent;

(b) Find the invariant measure of the chain (use the previous exercise);

(c) Determine the limit pn(i, j) when n .