Consider machine reliability, a DTMC with state space {0,1,2} with Yn= 0 if machine down, and Yn= 1 if machine is up at beginning of day n; and transition probability matrix:
P = .0009 .0582 .9409
.0006 .0488 .9506
.0004 .0392 .9604
Compute the probability that the number of working machines at the beginning of the next three days is two, one, and two in that order.