Let X be a Markov chain and let (nrr≥ 0} be an unbounded increasing sequence of positive integers. Show that Yr Xnr constitutes a (possibly inhomogeneous) Markov chain. Find the transition matrix of Y when nr = 2r and X is: (a) simple random walk, and (b) a branching process. =

Q: 2. Let Xo, X₁,... be the Markov chain on state space {1,2,3,4} with transition matrix 1/2 1/2 0 0…

A: Given that  be the Markov chain on state space  with transition matrix:

Q: 7. Let P = 14 4 be the transition matrix for a regular Markov chain. Find w1, the first component of…

A: none of the others.

Q: Q1: Prove (a) Markov's Inequality for non-negative continuous random variables U. (b) Chebeshey's…

A:

Q: A particle moves among the states 0, 1, 2 according to a Markov process whose transition probability…

A: Result If X be a Markov chain P(Xi=a|Xj=b)=[P(ba)]j-i Sum of row is 1.

Q: Let X₁, be the Markov chain with state space Z and transition probability P2,2+1 = P₁ P2,2-1 = 1- P₁…

A: a) The value of Y represents the first time the Markov chain reaches its minimum value. In this…

Q: True or False: Interaction variables violate the Gauss Markov assumption that our model should be…

A:

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A:

Q: Exercise #1 For the following Markov chain, determine: The long run fraction of the time that each…

A:

Q: Prove that the steady state probability vector of regular Markov chain is unique

A: The steady state probability vector of regular Markov chain is unique.

Q: Find the vector of stable probabilities for the Markov chain whose transition matrix is [0.4 0.6 1 1…

A: The answer is given as follows :

Q: A Doubly stochastic matrix is a stochastic matrix M of which the columns also sum to 1, i.e., Mij…

A: a) To show that the row vector  with entries for all is a stationary distribution for the Markov…

Q: Show that an irreducible Markov chain with a finite state space and transition matrix P is…

A:

Q: Consider the Markov chain X given by the diagram Write down the transition matrix 0 1 0 of the…

A:

Q: Consider a binary choice model in random utility framework: U1 = Bo + B1x1+ + Bræk + u = x'B+ u and…

A: Given:

Q: Q4) A Markov source as given in the table below: si S2 S3 P(S1)=0.2 P(S2)=0.2 P(S3)=0.6 PI2=0.3…

A: We have to find out :  Average source entropy We have to prove that :  G1>G2

Q: ocess into an irreducible Markov chain by asserting that if the population it, then the next…

A:

Q: A matrix is called Markov if all of its entries are positive and the sum of the entries of each row…

A: The given matrix is  A=0.9 0.10.3 0.7 A can be diagonalized if there exists an invertible matrix P…