A machine can be in one of three states: good, fair, and broken. When it is in a good condition, it will remain in this state for a time that is exponentially distributed with mean 1/μ 1 before going...

A machine can be in one of three states: good, fair, and broken. When it is in a good condition, it will remain in this state for a time that is exponentially distributed with mean 1/μ₁
before going to the fair state with probability 4/5 and to the broken state with probability 1/5. When it is in a fair condition, it will remain in this state for a time that is exponentially distributed with mean 1/μ₂
before going to the broken state. When it is in the broken state, it will take a time that is exponentially distributed with mean 1/μ₃
to be repaired before going to the good state with probability 3/4 and to the fair state with probability 1/4. What is the fraction of time that the machine is in each state?