--.*/ 'VOLC. .. A state vector X for a three-state Markov chain is such that the system is as likely to be in state 2 as in state 3 and is five times as likely to be in state 1 as in 2. Find the state vector X.
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Let the state vector be X = [ p1 p2 p3 ].
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- 2-Discuss in detail about "MARKOV'S PROCESS"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 processLet (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5} with X0 = 3 and transition matrix
- 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.A manufacturer has a machine that if it ran all day today has a proba- bility of 0.2 of breaking down sometime during the day tomorrow. When the machine breaks down, it goes offline for the remainder of the day and then a technician will spend the next day (after the breakdown) repairing it. A newly repaired machine only has a proability of 0.1 of breaking down sometime tomorrow. (a) Formulate the evolution of the status of the machine at the end of the day as a Markov Chain by identifying the three possible states at the end of the day and providing the transition probabilities between these states. (b) Determine the expected first passage times, µij , for all combinations of states i and j where i cannot equal to j (i.e., you don’t need to determine the recurrence times). You must provide the set of equations used to calculate these µij (micro with lowercase i and j). (c) Using your results from (b): (i) Identify the expected number of full days that the machine will remain…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?
- 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.Please don't copy Construct an example of a Markov chain that has a finite number of states and is not recurrent. Is your example that of a transient chain?Determine the classes of the Markov chain and whether they are recurrent.
- At any given time, a subatomic particle can be in one of two states, and it moves randomly from one state to another when it is excited. If it is in state 1 on one observation, then it is 3 times as likely to be in state 1 as state 2 on the next observation. Likewise, if it is in state 2 on one observation, then it is 3 as likely to be in state 2 as state 1 on the next observation. 1. Find the transition matrix for this Markov chain. 2. Based on this estimation, what is the probability that the particle will be in state 2 two weeks from now? 3. What is the probability that the particle will be in the state 1 three weeks from now?Construct a transition probability matrix of a Markov chain with state space {1, 2, . . . , 8} in which {1, 2, 3} is a transient class having period 3, {4} is an aperiodic transient class, and {5, 6, 7, 8} is a recurrent class having period 2.A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?
