A taxi moves between Imperial Airport Brawley Inn and the De

A taxi moves between Imperial Airport, Brawley Inn, and the DeAnza Hotel, with Markov model:

where position 1 is the airport, 2 is the Brawley Inn and 3 is the Hotel DeAnza.

a)   Over time, what fraction of visits will a taxi make to each of these locations?

b) If the taxi begins at the airport, what is the expected number of transitions (trips) that it will take for it to return to the airport.

Solution

b.)   p(i, i + 1) = 0.1, p(i, i 1) = 0.9, if 0 i N

N=3

starting :1 to 2=0.9 2 to 3=0.2 3 to 2=0.1 2 to 1=0.75