4.10. Consider a two-machine one-operator system. Let all times be exponentially distributed with mean rates: ( = 1, = 3, = 2/3) .

Set p(0,0,0) = 0.0842, and determine the next ten probabilities; that is, p(1,p,0) and then one set of three probabilities for each of the three equation-set forms similar to Eqs. (4.8)(4.10). PLEASE DO NOT USE CHATGBT.

Once the values of the probabilities (p(1,s,0),p(2,s,p),p(2,p,p)) have been obtained, the vector (p(2,s,s),p(3,s,p),p(3,p,p)) is solved similarly using the fifth through seventh equations in the system. This solution is written as Equations (4.5-4.7) can now be used to yield the general form of the solution for n3; namely p(n,s,s)p(n+1,s,p)p(n+1,p,p)=(+)00(+2)021p(n1,s,s)p(n1,s,p)+(++)p(n,s,p)p(n,p,p)