The eight vector corresponding to the unit eigenvalue is b/(a+b), a/(a+b) and as such ultimately the probability of the machines being found in working order is b/(a+b ) and the probability of its being found in a non-working state is a/(a+b).
| As a special
case, suppose we have a machine which can be in two states, working or non-working.
Let the probability of its transition from working to non-working be a,
of its transition from non-working to working be b,
then the transition probability matrix A
is obtained from the following formula, where the first column and row denote
working and the second, non-working.
The eight vector corresponding to the unit eigenvalue is b/(a+b), a/(a+b) and as such ultimately the probability of the machines being found in working order is b/(a+b ) and the probability of its being found in a non-working state is a/(a+b). |
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