Question 6 (25 points) [0.8 0.2 0 Given the following transition matrix, P = 0.3 0.5 0.2 with states 1, 2 & 3 representing brand 1, [0.1 0.1 0.8] brand 2 and brand 3. Each probability represents the likelihood of staying or switching brands after one month of advertising. Determine the following 1. Given a customer is currently using Brand 3, what is the probability of switching from Brand 3 to Brand 1 after 3 months of advertising? Show your Work (5 points) 2. Determine the steady state probabilities. Write the equations (10 points) 3. What is the average of months it takes a customer to return to brand 3, i.e. 33? (5 points) 4. On an average, how many months of advertising does it take to switch from Brand 1 to Brand 2? (5 points)