Chuck, Ted, and Sally are roommates and each day one of them must wash the dishes.
If Ted washes dishes one day, then Sally automatically does them the next day. If Sally washes dishes one day, then Chuck automatically washes dishes the next day. When Chuck washes dishes, there is a 25% chance that Sally will wash dishes the next day and a 75% chance that Ted will.
Write the transition matrix, T, for this scenario.
The methods for finding the steady-state distribution discussed in Section 6.3 only work with regular Markov chains. As you learned in the videos, a regular Markov chain is one where for some positive integer n, the matrix Tn has no zero entries. If you are told that this is a regular Markov chain and T is the transition matrix for this problem, find the smallest value of n for which the matrix Tn has no zero entries.