Unformatted text preview: 2. 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 ? 3. 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?) 1...
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 Fall '07
 Billings
 Markov chain, H. Ayhan

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