Math_303_Section_201_April_2008

Math_303_Section_201_April_2008 - Math 303. 25 April 2008....

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Unformatted text preview: Math 303. 25 April 2008. Final. MATH 303 Sect 201 2007/2008 README Fill this cover-page with your name and student number. Prepare to produce your ID upon request. Use the present sheets ONLY. Calculators, books, formula sheets and collaborations are NOT allowed. (In case of violation your work will be CONFISCATED). This exam has 6 problems (and some blank pages) Name: Number: P. 1: P. 2: P. 3: P. 4: P. 5: P. 6: Tot: 1 Math 303. 25 April 2008. Final. Problem 1 A Markov chain has space state { 1 , 2 , 3 , 4 , 5 , 6 } and transition matrix P = 3 / 4 1 / 4 2 / 5 1 / 5 2 / 5 2 / 3 1 / 3 2 / 7 5 / 7 1 1 a) Find the communicating classes. b) For each state of the chain, write, with a short explanation, if it is transient, null recurrent or positive recurrent. c) For each state of the chain, write, with a short explanation, the period. 2 Math 303. 25 April 2008. Final. Problem 2 Henry has three houses, one in Vancouver, one in Berlin and one in Prague, and he likes to spend some years in each of them. He may change place in the end of the year, and decides his destination according to the following rule:- if he has spent one year in Vancouver, for the next year he is equally likely to move to...
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Math_303_Section_201_April_2008 - Math 303. 25 April 2008....

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