Hi, I am having trouble with this problem:
There are two transmission lines from a generating station to a nearby city. Normally,
both are operating (up). On any day on which line A is operating, there
p that it will go down at the end of the day. On any day on which
line B is operating, there is probability q that it will go down at the end of the day.
It takes the repair crew a day to repair a broken line. Only one line can be repaired
at a time; if both are down, they repair line A first.
Model this situation as a Markov chain. (Hint: there are four states.)
I have the answer but I can't figure it out past probabilities p, q, & 1.
The answer is according to the transition diagram:
P= 1 p(1-q) q(1-p) pq
1-q 0 q 0
1-p p 0 0
0 0 1 0
I have drawn the state transition diagram, as well. I can easily see: p (prob line A will go down), q (prob line B will go down), and 1 (prob A repair) but I am lost after that. Do I have the states mixed up?
If p is the prob A will go down (state 3 to 2), I thought 1-p would be the prob A will go up (which would be transiton from state 2 to 1) but according to the solution the transition from 2 to 1 is 1-q.....
I'm soooo lost - can anyone put this in plain english for me.
The prof also said if we were having difficulty to set p=.01 and q =.02 and solve numerically but I have no idea how to do that.
Thanks very much