- Suppose that a Markov chain has the following transition matrixThe recurrent states area₁a₂00P = aza₁ az az a4 a50000as001000001 0000

Given a markov chain has the following transition matrix. We have to find the recurrent states.

Answered: Suppose that a Markov chain has the…

A First Course in Probability (10th Edition)

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Author:Sheldon Ross

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Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A factory worker will quit with probability 1/2 during her first month, with probability 1/4 during her second month and with probability 1/8 after that. Whenever someone quits, their replacement will start at the beginning of the next month. Model the status of each position as a Markov chain with 3 states. Identify the states and transition matrix. Write down the system of equations determining the long-run proportions. Suppose there are 900 workers in the factory. Find the average number of the workers who have been there for more than 2 months.
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2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix (1/2 1/2 0 0 1/7 0 3/7 3/7 1/3 1/3 1/3 0 0 2/3 1/6 1/6/ (a) Explain how you can tell this Markov chain has a limiting distribution and how you could compute it.
If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?
A Markov system with two states satisfies the following rule. If you are in state 1 then of the time you change to state 2. If you are in state 2 then of the time you remain in state 2. state 1 Write the transition matrix for this system using the state vector v state 2 T = Find the long term probability (stable state vector). vs
A Markov chain has two states. • If the chain is in state 1 on a given observation, then it is three times as likely to be in state 1 as to be in state 2 on the next observation. If the chain is in state 2 on a given observation, then it is twice as likely to be in state 1 as to be in state 2 on the next observation. Which of the following represents the correct transition matrix for this Markov chain? О [3/4 2/3 1/4 1/3 O [2/3 1/3 3/4 1/4) о [3/4 2/3 1/3] None of the others are correct 3/4 O [1/4 1/3 2/3. O [3/4 1/4] 1/3 2/3.
IN Markov process having transition matrix A = [a,k], whose entries are a11 = a12 = 0.6,a21 = 0.8, a22 = 0.8. and the initial state [0.7 0.8]T, SOLVE FOR the next 3 states.
Which of the following transition matrices is/are for a regular Markov Chain? 0 0 1 X = % 0 0 0 1 Y =|0 ½ ½ Z = % 0 2 (A) Y (В) X, Y (С) х (D) Y, Z (E) none (F) X, Z (G) (Н) Х, Y, Z
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Consider the Markov chain with three states,S={1,2,3}, that has the following transition matrix 1.Draw the state transition diagram for this chain. (10 marks)
2. For all permissible p values, determine the equivalence classes of the Markov chain with the following transition matrix P, classify states as transient or recurrent, and classify the Markov chain as irreducible or reducible. 0. 1-p 1 - 0. P = 0. 1-p 0. 1-p
Let {Xn: n = 0, 1, 2, ...} be a Markov chain with the four states 1,2,3,4. If p44 = 1, what is state 4 called? %3D an absorbing state O a certain state a recurring state O a cyclic state • Previous Simpfun

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Suppose that a Markov chain has the following transition matrix a az az a as a 4 000 The recurrent states are a₂000 P=a, 0 0 1 0 0 a000 as 1 0000