Suppose Xn, n = 0, 1, ... is a two-state Markov chain with states Sx = {0, 1}, whose transition probability matrix is0.10.90.95 0.05Then, Zn = (Xn-1, Xn), n = = 1,2,.That is, Zni j iff Xn-1i and XnPz===Px=is a four-state Markov chain with states Sz = {00, 01, 10, 11}.=j. Determine its transition probability matrix.

Suppose is a two state Markov chain with states whose transition matrix is given below:Let .

Answered: Suppose Xn, n = 0, 1, . . . is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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5. Suppose {Xn, n 2 0} is a Markov chain with state space (0, 1,2} and transition probability matrix 0.6 0.2 0.2 P= 0.8 0.2 0.5 0.5 Find the classes for this Markov chain and classify them as transient or recurrent.
7. The following 4-state Markov model with constant intensities a, B and y is used to model a pension scheme for male members aged 55. Age is defined as age last birthday on January 1". The states are w: Active, a: Preserved Benefit, b: Drawing pension and d: Dead. The following data were collected over an observation period covering a single calendar year on 1000 male members of the above pension scheme, all of whom are aged 55: Total waiting time in state w: 800 years Total number of transfers from state w to state a: 200 Total number of transfers from state w to state b: 200 Total number of transfers from state w to state c: 20 Find the likelihood function L(a, B.y) for these data and hence find the maximum likelihood estimates of a,ß and y.
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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.
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.
Suppose that a Markov chain with 3 states and with transition matrix P is in state 3 on the first observation. Which of the following expressions represents the probability that it will be in state 1 on the third observation? (A) the (3, 1) entry of P3 (B) the (1,3) entry of P3 (C) the (3, 1) entry of Pª (D) the (1,3) entry of P2 (E) the (3, 1) entry of P (F) the (1,3) entry of P4 (G) the (3, 1) entry of P2 (H) the (1,3) entry of P
If A is a Markov matrix, why doesn't I+ A+ A2 + · · · add up to (I -A)-1?
Let (X0, X1, X2, . . .) be the discrete-time, homogeneous Markov chain on state space S = {1, 2, 3, 4, 5, 6} with X0 = 1 and transition matrix
Give an example of one-step transition probabilities for a renewal Markov chain that is null recurrent.
Q3) The state transition matrix of a Markov random process is given by 1/3 1/3 1/6 1/6 5/9 0 0 4/9 2/5 1/5 1/5 1/5 0 0 3/20 17/20 [ ] Draw the state transition diagram and denote all the state transition probabilities on the same. Find P[X1 = 2] List the pairs of communicating states. Find P[X2 = 3| X1 = 2] Compute P[X2 = 2 | X0 = 1] Compute P[X3 = 3, X2 = 1, X1 = 2 | X0 = 3] (vii) Find P[X4 = 4, X3 = 3, X2 = 3, X1 = 1, X0 =2] where Xt denotes the state of the random process at time instant t. The initial probability distribution is given by X0 = [2/5 1/5 1/5 1/5].
Which of the following best describes the long-run probabilities of a Markov chain {Xn: n = 0, 1, 2, ...}? O the probabilities of eventually returning to a state having previously been in that state O the fraction of time the states are repeated on the next step O the fraction of the time being in the various states in the long run O the probabilities of starting in the various states • Previous Not saved Simpfun
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