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Unformatted text preview: Math331, Spring 2008 Instructor: David Anderson Section 5.3 Homework Answers Homework: pgs. 224  226, #s 3, 5, 9, 15, 17. 3. Let X be the number of times the professor tries the door until he is successful. Then we see that X is geometric with parameter p = 1 / 12. Therefore, to answer part (a) we simply need E [ X ] = 1 p = 12 . To find the probability that he opens his office door after only three tries we calculate P ( X = 3) = (1 p ) 2 p = parenleftbigg 11 12 parenrightbigg 2 1 12 . 07 . 5. The event that a given person has hazel eyes is a Bernoulli RV with p = . 2. Let X be the number of people that must board until we see the third person with hazel eyes. Then X is negative binomial with parameters p = . 2 and r = 3 and we are interested in P ( X = 8). Thus, P ( X = 8) = parenleftbigg 8 1 3 1 parenrightbigg (1 . 2) 8 3 ( . 2) 3 = parenleftbigg 7 2 parenrightbigg ( . 8) 5 ( . 2) 3 = 0 . 05505 ....
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 Spring '08
 Anderson
 Math, Probability

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