Question: Problem 3.1. Consider a continuous-time Markov chain on S = {1, 2, 3, 4} with generator matrix 1 0 0 -1 1 DOO Q 2

Problem 3.1. Consider a continuous-time Markov chain on S = {1, 2, 3, 4} with generator matrix 1 0 0 -1 1 DOO Q 2 -5 0 1 2 do (a) Write down the transition matrix of the associated embedded DTMC. (b) If the chain is currently in state 3, how long, on average will it take before moving to a new state? (c) If the chain is in state 3 at time t = 0, what is the probability that it remains there until at least time t = 2? (d) If the chain is currently in state 3 and its next move is to state 4, how long, on average, would you expect the chain to have stayed in state 3 before making that jump

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