The three largest categories of motor vehicles are sedan, SUV, and minivan. Suppose that of the buyers in a particular community who now own a minivan, 18% will change to an SUV and 20% will change to a sedan. Of the buyers who now own a sedan, 35% will change to a minivan and 20% will change to an SUV, and of those who now own an SUV, 12% will buy a minivan and 32% will buy a sedan.
a. Draw a transition diagram that displays these changes.
b. Write a transition matrix that represents this scenario. List the rows and columns in the order minivan, sedan, SUV.
c. What is the sum of the entries in row 1? Row 2? Row 3? Why does this sum make sense?