Find the equilibrium distribution of the Markov chain above
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A: Given information: The transition matrix is as given below:
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- 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.)Explain how you can determine the steady state matrix X of an absorbing Markov chain by inspection.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.
- (Exponential Distribution) must be about Markov Chain. The time between supernova explosions in the known universe is exponentially distributed with an average of 1 month. According to Mr. Spock, the spaceship Atlantic's scientist, a supernova explosion may deform the structure of the Higgs Boson, and may cause the extinction of the entire universe, with a probability of 1 in 118 billion. Assuming that the age of the universe is about 16 billion years, calculate the probability that such an event will cause the universe to disappear in the next 10 billion years.1/2 1/2 0 1/7 0 3/7 0 3/7 0 1/3 1/3 1/3 0 2/3 1/6 1/6,In the matrix 0.12 0.11 0.27 0.26 0.18 0.1 0.62 x 0.63 What should be the value of x so that P is a transition matrix rapresenting a Markov Chain. x= Number P =
- Find the vector of stable probabilities for the Markov chain whose transition matrix is 0. 0. 1 1 0.5 0.2 0.3The random variables W1, W2,... are independent with common distribution k 1 2 3 4 Pr( W = k) 0.1 0.3 0.2 0.4 Let Xn max (W1,..., Wn) be the largest W observed to date. Determine the transition probability matrix for the Markov chain {Xn}.A Markov chain has the transition probability matrix 0.3 0.2 0.5 0.5 0.1 0.4 [0.5 0.2 0.3 Given the initial probabilities o1 = ¢2 = 0.2 and ø3 0.6, what is Pr (Xı = 3, X2 = 1)? %3D
- 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.[.6 .3] .4 .7 Let P = be a transition matrix. Which one of the following vectors 10 4 is the steady-state vector for this transition matrix? Justify your response by demonstrating it is the steady- state vector by a computation that verifies the definition of steady-state vector.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}?
