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Unformatted text preview: STA 3007 Applied Probability 2005 Tutorial 4 1. First Step Analysis Exercise: i. Which will take fewer flips, on average: successively flipping a quarter until the pattern HHT appears, that is, until you observe two successive heads followed by a tails; or successively flipping a quarter until the pattern HTH appears? 1 ii. Consider the Markov Chain whose transition probability matrix is given by: P = 1 2 3 1 . . . . 1 . 1 . 2 . 5 . 2 2 . 1 . 2 . 6 . 1 3 . 2 . 2 . 3 . 3 Starting in state 1, determine the probability that the process never visits state 2. iii. An urn contains two red and two green balls. The balls are chosen at random, one by one, and removed from the urn. The selection process continues until all of the green balls have been removed from the urn. What is the probability that a single red ball is in the urn at the time that the last green ball is chosen?...
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This note was uploaded on 05/21/2011 for the course STA 3007 taught by Professor Kb during the Spring '11 term at CUHK.
- Spring '11