problemset09 - STAT/MA 416 Problem Set 9 Name 1 Butteries...

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STAT/MA 416 September 12, 2011 Problem Set 9 Name: 1. Butterflies. Alice, Bob, and Charlotte are looking for butterflies. They look in three separate parts of a field, so that their probabilities of success do not affect each other. Alice finds 1 butterfly with probability 17%, and otherwise does not find one. Bob finds 1 butterfly with probability 25%, and otherwise does not find one. Charlotte finds 1 butterfly with probability 45%, and otherwise does not find one. Let X be the number of butterflies that they catch altogether. Find the expected value of X . 1
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2. Dependence/independence among dice rolls. A student rolls a die until the first “4” appears. Let X be the numbers of rolls required until (and including) this first “4.” After this is completed, he begins rolling again until he gets a “3.” Let Y be the number of rolls, after the first “4”, up to (and including) the next “3.” E.g., if the sequence of rolls is 213662341261613 then X = 8 and Y = 7.
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