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Unformatted text preview: we see the ﬁrst kurrawong. 4 c) Let U be the distance (in miles) from 0 to the ﬁrst bird we see and V be the distance (in miles) from 0 to the ﬁrst bird of the other species (that is, if the ﬁrst bird we see is a kookaburra, then V is the distance to the ﬁrst kurrawong and vice versa ). Find the distribution of VU . 5 2) Consider the discrete time Markov chain X ,X 1 ,X 2 ,... with statespace { , 1 , 2 , 3 , 4 } and transition matrix 1 / 2 1 / 2 1 / 3 2 / 3 1 / 5 1 / 5 1 / 5 1 / 5 1 / 5 2 / 3 1 / 3 1 a) Which states are persistent and which states are transient? 6 b) What is the approximate value of P { X n = 0  X = 2 } when n is large? 7 c) Let T = min { n ≥ 1 : X n = 1 } . What is E [ T  X = 1]?...
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 Fall '05
 MONTEIRO
 Markov chain, discrete time Markov, certain fixed point, Steven Evans Instructions, Steven Evans

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