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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.Consider a continuous time Markov chain with three states {0, 1, 2} and transitions rates as follows: q01 = 3, q12 = 5, q21 = 6, q10 = 4 and the remaining rates are zeros. Find the limiting probabilities for the chain.suppose a continuous time markov process with three states s = {1, 2, 3} and suppose the transition rates q1,2, q2,3, q1,3, and q2,1 are non-zero, with all the other transition rates being zero. set up and solve the kolmogorov forward equations for this process
- Suppose that {Xn} is a Markov chain with state space S = {1, 2}, transition matrix （1/5 4/5 2/5 3/5）, and initial distribution P (X0 = 1) = 3/4 and P (X0 = 2) = 1/4. Compute the following: P(X2 =2)Suppose that a production process changes state according to a Markov chain on [25] state space S = {0, 1, 2, 3} whose transition probability matrix is given by a) Determine the limiting distribution for the process. b) Suppose that states 0 and 1 are “in-control,” while states 2 and 3 are deemed “out-of-control.” In the long run, what fraction of time is the process out-of-control?Consider a Markov chain {Xn}n≥0 having the following transition diagram: For this chain, there are two recurrent classes R1 = {6, 7} and R2 = {1, 2, 5}, and one transient class R3 = {3, 4}. Find the period of state Find f33 and f22. Starting at state 3, find the probability that the chain is absorbed into R1. Starting at state 3, find the mean absorbation time, i.e., the expected number of steps that the chain is absorbed into R1 or R2. Note: there are missing transition probabilities for this chain, but no impact for your solution.
- Show full answers and steps to part d) and e) using Markov Chain Theory. Please explain how you get to the answers without using excel, R or stataConsider the following stochastic system. Let Xn be the price of a certain stock (rounded to the nearest cent) at the time that the stock market closes on the n-th day starting today. Would it be appropriate to model this system as a Discrete-time Markov Chain?a) Suppose that whether or not it rains, today edpends on previous weather conditions through the last three days. Show how this system may be analyzed by using a Markov chain. How many states are needed? b) Suppose that if it has rained for the past three days, then it will rain today with probability 0.8; if it did not rain for any of the past three days, then it will rain today with probability 0.2; and in any other case the weather today will, with probibility 0.6, be the same as the weather yesterday. Determine P for this Markov chain.
- Suppose that X0, X1, X2, ... form a Markov chain on the state space {1, 2}. Assume that P(X0 = 1) = P(X0 = 2) = 1/2 and that the matrix of transition probabilities for the chain has the following entries: Q11 = 1/2, Q12 = 1/2, Q21 = 1/3, Q22 = 2/3. Find limn→∞ P(Xn = 1).Given the following Markov chain and the given recurrent classes {1,2}, {3,4} and {5,6}. Determine whether each recurrent class is periodic or aperiodic.2-Discuss in detail about "MARKOV'S PROCESS"