Maurice Tutor

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    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 31 Jan 2018 My Price 6.00

Markov chain

(a) Consider two urns A and B containing a total of N balls. An experiment is performed in which a ball is selected at random (all selections equally likely) at time t (f = 1, 2, ...) from among the totality of N balls. Then an urn is selected at random (A is chosen with probability p and B is chosen with probability q) and the ball previously drawn is placed in this urn. The state of the system at each trial is represented by the number of balls in A. Determine the transition matrix for this Markov chain.

 

(b) Assume that at time t there are exactly k balls in A. At time í -f-1 an urn is selected at random in proportion to its contents (i.e., A is chosen with probability k/N and B is chosen with probability (TV — k)/N). Then a ball is selected from A with probability p or from B with probability q and placed in the previously chosen urn. Determine the transition matrix for this Markov chain.

(c) Now assume that at time f + 1 a ball and an urn are chosen with probability depending on the contents of the urn (i.e., a ball is chosen from A with probability k/N or from B with probability (N — k)/N. Urn A is chosen with probability k/N or urn B is chosen with probability (N — k)/N). Determine the transition matrix of the Markov chain with states represented by the contents of A.

(d) Determine the equivalence classes in (a), (b), and (c).

Answers

Maurice Tutor
(5)
Status NEW Posted 31 Jan 2018 01:01 AM My Price 6.00

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