8 There are two machines. Machine i operates for an exponential time with rate λi and then fails, its repair time is exponential with rate µi , i = 1, 2. The machines act independently of each other. Define a four-state continuous time Markov chain that jointly describes the condition of the two machines. Use the assumed independence to compute the transition rates for this chain

Q: ou have a markov chain and you can assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix looks…

A: P(X0 = 1) = P(X0 = 2) = 12 P=12121323

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A: P=paapbapabpbb=1-p1p0 Here, the column sum is one. Since the system is in state A at time 0…

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A: The solution of the question is given below:

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Q: Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with -ix (1/2 1/2 0 0 1/7 0 3/7 3/7 0…

A: Given that  be the Markov chain on state space  with transition matrix:

Q: aving the four states (0, 0), (0, 1), (1, natrix.

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Q: Then, what does the equation, d/dt Π = MΠ means? (where M is a 4x4 transition rate matrix)

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A: *Answer:

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