Reconsider Prob. 29.2-1.
(a) Use the procedure Chapman-Kolmogorov Equations in your IOR Tutorial to find the n-step transition matrix P(n) for n = 2, 5, 10, 20.
(b) The probability that it will rain today is 0.5. Use the results from part (a) to determine the probability that it will rain n days from now, for n = 2, 5, 10, 20.
(c) Use the procedure Steady-State Probabilities in your IOR Tutorial to determine the steady-state probabilities of the state of the weather. Describe how the probabilities in the n-step transition matrices obtained in part (a) compare to these steady-state probabilities as n grows large.