For the random walk of Example 4.13 use the strong law of large numbers to give another proof that the Markov chain is transient when pt. Hint: Note that the state at time n can be written as 27, Y, where the Y's are independent and P(Y, 1) p 1-P{Y=-1). Argue that if p>, then, by the strong law of large numbers, Yoo as co and hence the initial state 0 can be visited only finitely often, and hence must be transient. A similar argument holds when p < .