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Unformatted text preview: STAT/MA 416 September 14, 2011 Problem Set 10 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. Write X as the sum of three indicator random variables, X 1 ,X 2 ,X 3 that indicate whether Alice, Bob, Charlotte (respectively) found a butterfly. Then X = X 1 + X 2 + X 3 . Find the expected value of X by finding the expected value of the sum of the indicator random variables. 1 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.” LetAfter this is completed, he begins rolling again until he gets a “3....
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- Fall '08
- Probability, Probability theory, Dice