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Unformatted text preview: X n denote the number of black balls in urn 1 after stage n has been performed. 1. Compute the transition probabilities of the Markov chain X n . 2. Without computation, what are the limiting probabilities of this chain (steady state distribution)? 3. Compute the limiting distribution and show that the chain is reversible. Problem 4: (Problem 78, p. 279) ±or the Markov chain with transition matrix 1 2 1 3 1 6 1 3 2 3 1 2 1 2 suppose that p ( s | j ) is the probability that signal s is emitted when the underlying MC state is j , j = 0 , 1 , 2. 1. What proportion of emissions are signal s ? 2. What proportions of those times in which signal s is emitted is 0 the underlying state? Problem 5: (Problem 64, p. 275) Consider a branching process with μ < 1. Show that if X = 1, then the expected number of individuals that ever exist in this population is given by 1 1-μ ....
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This note was uploaded on 04/15/2010 for the course STAT 416 taught by Professor Denker during the Spring '08 term at Pennsylvania State University, University Park.
- Spring '08
- Stochastic Modeling