Consider the pair of Ehrenfest urns studied in Section 10.2, Exercise 9. Suppose that there are now
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Consider the pair of Ehrenfest urns studied in Section 10.2, Exercise 9. Suppose that there are now 2 molecules in urn A. How many steps on average will be needed until there are again 2 molecules in urn A?
Data From Section 10.2 Exercise 9
Consider a pair of Ehrenfest urns with a total of 4 molecules divided between them.
a. Find the transition matrix for the Markov chain that models the number of molecules in urn A, and show that this matrix is not regular.
b. Assuming that the steady-state vector may be interpreted as occupation times for this Markov chain, in what state will this chain spend the most steps?
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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