Question

The math office has some markers in a closet. Math faculty use the markers in rooms 214, 216, and 317.

Every day, 30% of the markers in the closet are taken out and evenly distributed to the three classrooms (i.e. 10% per room).

Every day, the faculty teaching in room 214 don’t think that they have enough markers, so they take 20% of the markers in room 216.

Every day, the faculty teaching in room 216 don’t think that they have enough markers, so they take 30% of the markers in room 214.

Every night, the marker goblins emerge and bring 20% of the markers in each classroom back into the math office closet.

Construct a stochastic matrix P for this Markov chain. Show that this matrix is regular, and then find its unique steady-state vector. If there are 35 markers total in the these rooms, how many will end up in each room/closet in the long-term?

Answer 1