-A taxi is located either at the airport or in the city. From the city, the next trip is to the airport with 1/4 probability, or to somewhere else in the city with 3/4. From the airport, the next trip is always to the city.
(a) find the stationary distribution
(b) starting from the airport, what is the expected number of trips until its next visit to the airport?
The Attempt at a Solution
The matrix I got is
but I am having trouble solving for the stationary distribution and expected number of trips. Somehow, I don't think the stationary distribution even exists. But it should. What am I missing? Thanks.