= (b) The following is a Markov (migration) matrix for 3 locations 1, 2, and 3....
1. (3 pts) Let 10 0 0 0 -1 A = Find the minimal polynomial for A. 2. (3 pts) Suppose that the migration matrix for three locations is .5 0 3 3 8 0 .2 2 .7 Find a comparison for the population in the three locations after a long time.
1). Consider a Markov system modelling the migration of people with 2 states: a person can either be in town A or in town B. Every year, a person from town A has 20% chance of moving to town B, and a person from town B has a 35% chance of moving to town A. (a) If there were 20000 of people in Town A and 15000 of people in Town B initially, find the number of people in Town...
Consider a Markov system modelling the migration of people with 2 states: a person can either be in town A or in town B. Every year, a person from town A has 20% chance of moving to town B, and a person from town B has a 35% chance of moving to town A. (a) If there were 20000 of people in Town A and 15000 of people in Town B initially, find the number of people in Town A...
(2) Suppose you have a Markov chain with 3 states, with the following transition prob- ability matrix: 2/3 1/3 1/3 1/3 1/2 1/2 (a) If you start in state 1, what is the chance you will be in state 3 after one step? 1/3 0 0 (b) If you are equally likely to start in any state, what's the likelihood you are in state 2 after one step? (c) After 1000 steps, what's the chance the you are in state...
P is the (one-step) transition probability matrix of a Markov chain with state space {0, 1, 2, 3, 4 0.5 0.0 0.5 0.0 0.0 0.25 0.5 0.25 0.0 0.0 P=10.5 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.5 0.5 0.0 0.0 0.0 0.5 0.5/ (a) Draw a transition diagram. (b) Suppose the chain starts at time 0 in state 2. That is, Xo 2. Find E Xi (c)Suppose the chain starts at time 0 in any of the states with...
1. Consider a Markov chain (X) where X E(1.2,3), with state transition matrix 1/2 1/3 1/6 0 1/4 (a) (6 points) Sketch the associated state transition diagram (b) (10 points) Suppose the Markov chain starts in state 1. What is the probability that it is in state 3 after two steps? (c) (10 points) Caleulate the steady-state distribution (s) for states 1, 2, and 3, respee- tively 1. Consider a Markov chain (X) where X E(1.2,3), with state transition matrix...
A4. Classify the states of the Markov chain with the following transition matrix. 0 3 0 1 Find the stationary distribution of each irreducible, recurrent subchain and hence obtain the mean recurrence time of each state. (8
Consider a Markov chain {YmJnEN with state space S ,2, 3, 4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 00 1/6 1/2 1/3 0 0 4/9 4/9 1/9 0 0 5/6 1/6 (a) Find the equilibrium probability distribution π (b) Find the probability PO1 3. Уг 3.Ý, 1) Consider a Markov chain {YmJnEN with state space S ,2, 3, 4), initial distribution Po (0.25,0.25, 0.5,0), and transition matrix 1/3 2/3 00 1/6 1/2 1/3 0 0 4/9...
2. Consider a Markov chain with state space S 1,2,3,4) with transition matrix 1/3 2/3 0 0 3/4 1/4 00 0 0 1/5 4/5 0 0 2/3 1/3, (a) (10 points) Is the Markov chain irreducible? Explain your answer ive three examples of stationary distributions.
Consider a Markov chain with state space S = {1, 2, 3, 4} and transition matrix P= where (a) Draw a directed graph that represents the transition matrix for this Markov chain. (b) Compute the following probabilities: P(starting from state 1, the process reaches state 3 in exactly three time steps); P(starting from state 1, the process reaches state 3 in exactly four time steps); P(starting from state 1, the process reaches states higher than state 1 in exactly two...