Question

r. Harsy's beloved cat Archer's daily activities can be modeled by a Markov Process. At any given hour, he will either be napping on Dr. Harsy's computer, watching the birds, or playing sister kitty, Eva. If Archer is napping, he is 25% likely to continue napping the next cher is napping, he is 35% likely to be watching birds the next hour. If Archer is wratching birds, he is 60% likely to be napping the next hour and 30% likely to continue hing birds the next hour. If Archer is playing with Eva, he is 40% likely to be napping hour. If Ar watc the next hour and 30% likely to be watching birds during the next hour. (a) (4 points) Create the Transition Matrix that represents Archer's "states." Hint: Remember when creating your transition matrix, you construct it so each entry gives the probability of moving from the column state to the row state. (b) (5 points) If Archer is watching birds, what is the probability that he is napping 3 hours from now? (c) (6 points) Find a nontrivial steady-state vector for the system.

Answer 1

The states are 0, 1, 2 when 0 is Archer is napping for watching birds, 2 for playing with Eva P_00 = 25/100 P_01 = 35/100 P_10 = 60/100 P_11 = 30/100 P_20 = 40/100 P_21 = 30/100 P_02 = 40/100 = 1 - (P_00 + P_01) P_12 = 10/100 = 1 - (P_11 + P_10) p_22 = 30/100 = 1 - (P_20 + P_21) since row sum = 1 Therefore The transition matrix that represents state is P = (25/100 35/100 40/100 60/100 30/100 10/100 40/100 30/100 30/100) P is the one step transition matrix P^(3)_10 = Probability that Archer is napping 3 hours from now provided he is watching birds