Question: I need help with the following problem Problem 2. Continuous-time Markov chain (20 pts) We consider a continuous-time Markov chain (X1) >with infinitesimal generator given

I need help with the following problem

Problem 2. Continuous-time Markov chain (20 pts) We consider a continuous-time Markov chain (X1) >with infinitesimal generator given by -21 0 0 0 1 1 0 (a) How long do you wait on average at state #1 before moving to another state? (b) Determine the transition matrix P of the embedded chain. Is the embedded chain ergodic? (c) How many steps does it take on average before the embedded chain reaches state #2 ? (d) How much time does it take on average before the chain (X) reaches state #2 ? (e) We consider what happens at time t = ln(2). Determine the distribution of Xin(2) given that Xo = 1. Problem 2. Continuous-time Markov chain (20 pts) We consider a continuous-time Markov chain (X1) >with infinitesimal generator given by -21 0 0 0 1 1 0 (a) How long do you wait on average at state #1 before moving to another state? (b) Determine the transition matrix P of the embedded chain. Is the embedded chain ergodic? (c) How many steps does it take on average before the embedded chain reaches state #2 ? (d) How much time does it take on average before the chain (X) reaches state #2 ? (e) We consider what happens at time t = ln(2). Determine the distribution of Xin(2) given that Xo = 1

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