Suppose that in a Markov chain Xn, n 2 0 the state is transient with pn > 0. Let denote the total number of visits to during the whole path XO,XI , X2, .... Show that has geometric distribution if the Markov chain starts from r. Hint: Compute P(N(:r) = k). A random variable T has geometric distribution with param- eter p (O, l) if P (T = k) = for k {l, 2,