Suppose that in a Markov chain X\

Suppose that in a Markov chain Xn, n 2 0 the state is transient with pac > 0. Let N@) denote the total number of visits to during the whole path Xo, Xl, X2, .... Show that N@) has geometric distribution if the Markov chain starts from T. Hint: Compute P(N@) = k). A random variable T has geometric distribution with param- eter p e (0, 1) if P (T = k) = p(l I forke {1, 2, .