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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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
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.
A state vector X for a four-state Markov chain is such that the system is three times as likely to be in state 4 as in 3, is not in state 2, and is in state 1 with probability 0.2. Find the state vector X.
12. A stochastic matrix Pis called doubly stochastic if Σi Pij = 1 for all j. It is called sub-stochastic if Ei Pij ≤ 1 for all j. Show that, if P is stochastic (respectively, doubly stochastic, sub-stochastic), then Pn is stochastic (respectively, doubly stochastic, sub-stochastic) for all n.

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