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Unformatted text preview: STAT 333 Assignment 3 Due: Monday, Dec. 6 in MC6095 between 1:00 to 3:00 (Please print) Last name: First Name: ID#: Acknowledgements: Mark: TAs initials: 1. Consider a random walk on the integers, starting at 5. The random walk jumps to the right with probability 0 . 65. (1) What is the probability of a return to the starting position 5? (2) What is the expected number of returns to 5? (3) What is the probability that the walk ever visits 10? (4) What is the expected number of jumps required for the walks first visit to 10? (5) What is the probability that the walk ever visits 0? (6) What is the expected number of visits to 10? (7) What is the expected number of visits to 0? (8) What is the probability that the walk will hit 10 before it hits state 0?(Gamblers ruin) (9) Suppose the walk is balanced, i.e. p = 0 . 5, and the walk currently at stat 5. What is the probability that the walk will hit 10 before it hits state 0?(Gamblers ruin) 2. Consider a Markov chain on S = { , 1 , 2 , 3 , 4 , 5 } , whose transition matrix is P =...
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 Fall '10
 MenZhongxian
 Probability, Probability theory, Exponential distribution, Markov chain, Tim Horton

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