A continuous-time Markov chain (CTMC) has the following Q = (qij) matrix (all rates are transition/second)
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.There are two printers in the computer lab. Printer i operates for an exponential time withrate λi before breaking down, i = 1, 2. When a printer breaks down, maintenance is called to fix it,and the repair times (for either printer) are exponential with rate μ. (a) Can we analyze this as a birth and death process? Briefly explain your answer.(b) Model this as a continuous time Markov chain (CTMC). Clearly define all the statesand draw the state transition diagram.43.10. Permanent disability is modeled as a Markov chain with three states: healthy (state 0), disabled (state 1), and dead (state 2). You are given the following transition forces: 0.05 5 (1) = 0.10 r>5 (i) 4, =0.02 (iii) p,-0.02 Calculate the probability that a healthy person age x will be dead at age x +10.
- The transition matrix of a Markov chain is given by 0 0 P = (a) Find two distinct stationary distributions of this Markov chain. (b) Find the general form of the stationary distribution. (c) If 70) = (, 4, ¿, 1, ) is the initial probability vector at time 0, ,π(m) = (금' 등,을 ,). 4'4'6' 6' 6 then show that limn 12 HIN O -160 2/3 HIN O 230116 O 0 -16 0 116Please show steps to find solution for markov chainFind the vector of stable probabilities for the Markov chain whose transition matrix is 0 1 0.1 0.7 0.2 1 -( W =
- Consider the two state switch model from the videos with state space S = {1,2} and transition rate matrix where X = 1 and u = 1.2. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (c) Evaluate P11 (0.6) Number (d) Evaluate P21 (0.6) NumberAn individual can contract a particular disease with probability 0.17. A sick person will recover dur- ing any particular time period with probability 0.44 (in which case they will be considered healthy at the beginning of the next time period). Assume that people do not develop resistance, so that pre- vious sickness does not influence the chances of contracting the disease again. Model as a Markov chain, give transition matrix on your paper. Find the probability that a healthy individual will be sick after two time periods.Consider the two state switch model from the videos with state space S = {1,2} and transition rate matrix where A = 1 and u = 1.5. (a) If the system is in state 1, what is the mean time until it transitions to state 2? Number (b) Evaluate P11 (0) Number (C) Evaluate P11 (0.4) Number (d) Evaluate P21 (0.4) Number
- Suppose that a Markov chain has transition probability matrix 1 2 1 P (1/2 1/2 2 1/4 3/4 (a) What is the long-run proportion of time that the chain is in state i, i = 1,2 ? 5. What should r2 be if it is desired to have the long-run average (b) Suppose that ri reward per unit time equal to 9?What is the stable vector of this Markov chain?Find the 3-step transition matrix.