***Please state all assumptions, equations used, and work done***

Each American family is classified as living in an urban, rural, or suburban location. During a given year, 15% of all urban families move to a suburban location, and 5% move 10 a rural location; also, 6% of all suburban families move 10 an urban location, and 4% move to a rural location; finally, 4% or all rural families move to an urban location, and 6% move to a suburban location.

1. Construct the (one-step) transition matrix (15 points).
2. Suppose that at present, 40% of all families live in an urban area, 35% live in a suburban area, and 25% live in a rural area. Two years from now, what percentage of American families will live in an urban area? (15 points).
3. Calculate the first passage time that families will move to a rural area from all others (20 points).