5. Markov Chain You are given the following transition matrix for a Markov chain with state space S = {1, 2}. P = °- (17º 129). for 0 < p, q≤1. Does the Markov chain have a limiting distribution? Make an analysis depending on the value of p and q
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- Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.12. Robots have been programmed to traverse the maze shown in Figure 3.28 and at each junction randomly choose which way to go. Figure 3.28 (a) Construct the transition matrix for the Markov chain that models this situation. (b) Suppose we start with 15 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)Give me right solution according to the question
- Give two interpretation of what the first entry of the distribution (the limiting distribution of the markov chain) tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology. Both interpretations should be written in this way.Plz don't give solution in image format and give me solutions as soon as possibleLet {X„} be a time homogeneous Markov Chain with sample space {1,2, 3, 4} and transition matrix P = Does this Markov Chain converge to a stationary distribution? If it does, find the stationary distribution. If not, explain. O -131 3
- Find the limiting distribution for this Markov chain. Then give an interpretation of what the first entry of the distribution you found tells you based on the definition of a limiting distribution. Your answer should be written for a non-mathematician and should consist of between 1 and 3 complete sentences without mathematical symbols or terminology.The transition matrix of a Markov Process is given by 7 9 10 10 T 1 3 10 10 V1 The steady state probability distribution vector for this Markov Process is denoted by v = v2 Hence v1 + v2 = Number Making use of the above condition and solving a matrix equation, find the values of v1 and vɔ. Enter their exact values in the boxes below. v1 v2 =Let Zm represent the outcome during the nth roll of a fair dice. Define the Markov chain X, to be the maximum outcome obtained so far after the nth roll, i.e., X, = max {Z1, Z2,..., Zn}. What is the transition probability p22 of the Markov chain {Xn}?
- Let X be a random variable with sample space {1,2, 3} and probability distribu- (G 1 ). Find a transition matrix P such that the Markov chain {X„} tion T = simulates X.Let P = (0.9 0.9 0.1 0.2 0.8 with two states A and B. be a transition matrix for a Markov Chain 1. What proportion of the state A population will be in state B after two steps Number 2. What proportion of the state B population will be in state B after two steps Number 3. Find the steady state vector x x1= Number X2= Number Write the results accurate to the 3rd decimal placeSuppose 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?
