Question: Note that the transition RATE matrix is given, not the transition probability matrix. 2. (50pts) A continuous time Markov process with states 1,2,3,4, and 5

Note that the transition RATE matrix is given, not the transition probability matrix.

2. (50pts) A continuous time Markov process with states 1,2,3,4, and 5 has the transition rate matrix shown below. All rates are expressed in terms of minutes. =6000043000023000120020100 (a) If the process begins in state 1 , what is the mean time accumulated in state 2 ? (b) If the process begins in state 1 , what is the probability that it ends up in state 4 ? (c) If the process is in state 1 , what is the probability that it will reach state 3 at some point? (d) If the process is in state 2, what is the average time that the process continues before it terminates

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