Suppose that a Markov process is given by the rule Xn+1 = Axn, where A is a stochastic matrix and xn is thestate vector after n time periods of the process.Which of the following statements must be true?Select one alternative:The entries in each row of A add to 1.O The entries in each column of A add to 1.O The columns of A form a linearly independent set.O A is an orthogonal matrix.

In a right stochastic matrix rows add to 1. In a left stochastic matrix column add to 1.

Answered: Suppose that a Markov process is given…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question 1.16.2 (Markov chains, Part IB, 1991, 307D) Three girls A, B and C are playing table tennis. In each game, two of the girls play against each other and the third girl does not play. The winner of any given game n plays again in game n + 1. The probability that girl x will beat girl y in any game that they play against each other is sx/(Sx+Sy) for x, y = {A,B,C}, x‡y, where sa, SB, SC represent the playing strengths of the three girls. In what proportion of games does each girl play, in the long run?
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2. Determine whether or not the given matrix is stochastic. If so, determine if it is regular, absorbing, or neither. 01 0 6173 213
Determine whether the stochastic matrix P is regular. [ 0.2 0.1 P = 0.8 0.9 regular O not regular Find the steady state matrix X of the Markov chain with matrix of transition probabilities P. (If the system has an infinite number of solutions, express x1, and x2 in terms of the parameter t.) X = 0.5
Suppose that a Markov chain has the following transition matrix a, az az as a s 3 000 The recurrent states are a 4 4 a₂000 P=a₂00 0 0 a003 as 1 0 0 0
DO NOT COPY OTHER SOLUTIONS. USE A TRANSITION PROBABILITY MATRIX WHEN SOLVING. Consider the following Markov chain. Assuming that the process starts in state 4, what is the probability that we eventually reach the recurrent class {1,2}?
Consider the migration (Markov) matrix A = 0.7 0 0.2 0.1 0.4 0.2 0.2 0.6 0.6 Suppose that, initially, there are 96 residents in location 1, 82 residents in location 2, and 151 residents in location 3. Assume time is measured in years. Find the population in each location after 1 year. Find the population in each location after 2 years.
3. suppose that the manufacturer keeps a spare machine that only is used when the primary machine is being repaired. During a repair day, the spare machine has a probability of 0.1 of breaking down, in which case it is repaired the next day. Denote the state of the system by (x, y), where x and y, respectively, take on the values 1 or 0 depending upon whether the primary machine (x) and the spare machine (y) are operational (value of 1) or not operational (value of 0) at the end of the day. [Hint: Note that (0, 0) is not a possible state.] (a) Construct the (one-step) transition matrix for this Markov chain. (b) Find the expected recurrence time for the state (1, 0).
1. Indicate whether each statement is true or false. No justification is necessary.
Suppose in a scatterplot matrix, you observe that all of the scatterplots associated with the explanatory variables show a strong linear relationship. There are three explanatory variables in the model. Of the following, which is the most valid to do? Remove the response variable. Remove only one of the explanatory variables and keep only two. Remove all of the explanatory variables because they are linearly related to each other and therefore explain the same thing. Remove exactly two of the explanatory variables because they are all linearly related to each other and therefore explain the same thing. We only need to keep one in the model.
C, D And E please!
Determine whether the statement below is true or false. Justify the answer. If (x) is a Markov chain, then X₁+1 must depend only on the transition matrix and xn- Choose the correct answer below. O A. The statement is false because x, depends on X₁+1 and the transition matrix. B. The statement is true because it is part of the definition of a Markov chain. C. The statement is false because X₁ +1 can also depend on X-1 D. The statement is false because X₁ + 1 can also depend on any previous entry in the chain.

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