Find the n-step transition probabilities pij (n) for the chain X having transition matrix P= 0 1/3 23 121414 125212
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- Find the 3-step transition matrix.3.4 Consider a Markov chain with transition matrix 1- a a P = 1-b b 1-c where 0< a, b, c < 1. Find the stationary distribution.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.
- Suppose the transition matrix for a Markov Chain is T = stable population, i.e. an x0₂ such that Tx = x. ساله داد Find a non-zeroConsider a binary choice model in random utility framework: U1 = Bo + B1x1 + · ·. + BrXk + u = x'B+u and Uo = 0, where Uj and Uo are utilities from y = 1 and y = 0. When u follows the standard logistic distribution [the CDF of u is A(u) 1+e« ], what is the partial effect from a1 on the choice probability of choosing 1? B1 A(x'B)B1 A(x'B)[1 – A(x'B)]B1Consider 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) 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?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.According to data collected during one year in a large metropolitan community, 30% of commuters used public transportation to get to work, and this rose by 4% the following year. This is modeled by the transition matrix P P' M= P P' 0.9 0.1 0.1 0.9 , So = [0.3 0.7] where P represents the percentage of people that use public transportation and P' the percentage of people that do not. What percentage of commuters in this communit will use public transportation in the long run? Round the percent to the nearest tenth. O A. 50.0% OB. 37.2% O C. 34.0% O D. 30.0% C
- 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) NumberFind the steady-state vector for the transition matrix in the attached picture. Thanks.Consider a Markov chain {X, : n = 0, 1, - .-} on the state space S = {1,2,3,4} with the following transition matrix: 1/3 2/3 1/2 1/2 P = 1/4 3/4 1/4 1/4 1/2 Find Pr(X7 = 2|X1 = 3). %3D Determine the class(es) of the above Markov chain. Specify which state is recurrent and which state is transient. Justify your results.