Question: Consider a machine that breaks down on a given day with probability p. A repair can be completed in 1, 2, 3, or 4 days

Consider a machine that breaks down on a given day with probability p. A repair can be completed in 1, 2, 3, or 4 days with respective probabilities q₁, q₂, q₃, and q₄. The condition of the machine can be represented by one of the following five states:

State 0 (W) Working 1 (D1) Description Not Working, in first day

Since the next state of the machine depends only on its present state, the condition of the machine can be modeled as a five state Markov chain.

Construct the transition probability matrix.

State 0 (W) Working 1 (D1) Description Not Working, in first day of repair 2 (D2) Not Working, in second day of repair 3 (D3) Not Working, in third day of repair 4 (D4) Not Working, in fourth day of repair

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