Unformatted text preview: { X 4 = 3 ,X 1 = 5  X 2 = 6 } 3. A sixsided die is rolled repeatedly. After each roll n = 1 , 2 ,... , let X n be the largest number rolled in the ﬁrst n rolls. Is { X n ,n ≥ 1 } a discretetime Markov chain? If it’s not, show that it is not. If it is, answer the following questions: (a) What is the state space and the transition probabilities of the Markov chain? (b) What is the distribution of X 1 ? 4. Redo the previous problem except replace X n with Y n where Y n is the number of sixes among the ﬁrst n rolls. (So the ﬁrst question will be, is { Y n ,n ≥ 1 } a discretetime Markov chain?)...
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 Spring '07
 Billings
 Markov chain, Stochastic Manufacturing, discretetime Markov chain

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