b) and c)

1) Consider the following situation involving Bus Transportation and answer the questions that follow: There are 4 bus routes from East end to Downtown. After collecting data, the monthly trend shows: i) Of the riders that took Route 1, 40% of riders would switch to Route 2, 30% would switch to Route 3, and 10% would switch to Route 4. ii) of the riders that took Route 2, 70% of riders would switch to Route 1, 10% would switch to Route 3, and 10% would switch to Route 4. i) of the riders that took Route 3,60% of riders would switch to Route 1, 10% would switch to Route 2, and 10% would switch to Route 4. iv) of the riders that took Route 4, 20% of riders would switch to Route 1, 20% would switch to Route 2, and 10% would switch to Route 3. A) Construct the Markov Matrix that describes this example. [4 Marks) B) There also happens to be 3 routes from the West end to Downtown. When diagonalizing the Markov Matrix from the West end to Downtown we get: 53-1 3 0 A = PDP-1 where P = 4 0-41 D = 10 0.4 11 0 0.6) lano 0 0 0 1 LO PX11 10001 If today, the current distribution of riders for each route is x2 = 2000, determine what will happen in the 5000 long run in terms of riders from each route in the west end. [5 Marks) C) What do you notice about your answer in B and the eigenvector for 1 = 1. Explain why this should have happened using a theorem discussed in class. [3 Marks) 1) Consider the following situation involving Bus Transportation and answer the questions that follow: There are 4 bus routes from East end to Downtown. After collecting data, the monthly trend shows: i) Of the riders that took Route 1, 40% of riders would switch to Route 2, 30% would switch to Route 3, and 10% would switch to Route 4. ii) of the riders that took Route 2, 70% of riders would switch to Route 1, 10% would switch to Route 3, and 10% would switch to Route 4. i) of the riders that took Route 3,60% of riders would switch to Route 1, 10% would switch to Route 2, and 10% would switch to Route 4. iv) of the riders that took Route 4, 20% of riders would switch to Route 1, 20% would switch to Route 2, and 10% would switch to Route 3. A) Construct the Markov Matrix that describes this example. [4 Marks) B) There also happens to be 3 routes from the West end to Downtown. When diagonalizing the Markov Matrix from the West end to Downtown we get: 53-1 3 0 A = PDP-1 where P = 4 0-41 D = 10 0.4 11 0 0.6) lano 0 0 0 1 LO PX11 10001 If today, the current distribution of riders for each route is x2 = 2000, determine what will happen in the 5000 long run in terms of riders from each route in the west end. [5 Marks) C) What do you notice about your answer in B and the eigenvector for 1 = 1. Explain why this should have happened using a theorem discussed in class. [3 Marks)