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Unformatted text preview: Stat 230 Winter 2008 1. [12 Marks] The letters of the word SUCCESSES are arranged at random, in a row. (a) Find the probability that the letters appear in alphabetical order. (b) Find the probability that S occurs at the start or the end but not both. (c) Now consider arranging the letters on a circle instead of in a row. Find the probability the 4 S’s are NOT together. Page 1 of 14 Stat 230 Winter 2008 2. [10 Marks] Tim is investigating wolves, coyotes and crossbreeds in Algonquin park. We will call any of these three animals (wolves, coyotes or crossbreeds) a canine. We assume that the appearence of a canine is independent of the appearance of another. We also assume canines appear singularly (not in groups) and on average 4 can be seen on any particular day. Finally we assume that a particular canine can appear more than once. He has found an area where there are 12 wolves, 6 wolfcoyote crossbreeds and 2 coyotes. (a) What is the probability that Tim sees 5 canines on any particular day? (b) Tim sees 5 canines during the day. What is the probability that 2 of them were wolves and 1 of them was a coyote? (c) Tim sees 5 canines during the day. What is the probability he sees at least 4 wolves? Page 2 of 14 Stat 230 Winter 2008 (d) What is the probability it takes Tim until he sees his 6th canine before he sees his third wolf? (e) If Tim randomly traps and retains 5 canines during the day , what is the probability he traps and retains at least 4 wolves? 3. [4 Marks] Let a be a constant and X a random variable (r.v.)....
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 Fall '06
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 Probability, Variance, Probability theory, Tim

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