Question

A car rental agency has rental and return facilities at both Dallas and Austin Airports. Assume that a car rented at either airport must be returned to one or the other airport. If a car is rented at Austin, the probability that it will be returned there is .80; If a car is rented at Dallas, the probability that it will be returned there is .70. Assume that the company rents all 100 cars each day and each car is only returned once each day. If we start with 50 cars at each airport: Create the transition matrix. 2. what is the expected distribution the next day? after 2 days?

Answer 1

transition matrix:

.8 .2
.7 .3

so
[.5 .5 ]
x
.8 .2
.7 .3
=
[.75 .25) next day

after 2 days:
[.75 .25]
x
.8 .2
.7 .3
= [.775 .225]