Question 2:

Assume that a person's last cola purchase was Coke, there is an 8- % chance that his next cola purchase will also be Coke. If a person's last cola purchase was Pepsi, there is a 60% chance that his next cola purchase will also be Pepsi. Use the Markov matrix to solve the following two parts...

(a) If a person is currently a Pepsi purchaser, what is the probability that he will purchase Pepsi six purchases from now?

(b) If a person is currently a Coke purchaser, what is the probability that he will purchase Coke four purchases from now?

(Use MATLAB for matrix calculation such as matrix multiplication and power.) Hint: To solve this problem, you need to determine the states (S), the transition matrix (T), and the initial distribution vector (Po) first.