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Unformatted text preview: Stat 333 : Tutorial 5  Fall 2011 1. In Mystic Falls, three people, Klaus, Damon and Stefan are searching for Elena, indepen dently of the other. Both Stefan and Damon must find Elena before Klaus does; otherwise, if Klaus finds her before either Stefan or Damon (or both), she will die. The times taken to find Elena are denoted as • X 1 for Stefan, where X 1 ∼ Exp ( 1 6 ) , • X 2 for Damon, where X 2 ∼ Exp ( 1 5 ) , • X 3 for Klaus, where X 3 has a p.d.f f X 3 ( x ) , x ≥ . (a) Find the joint distribution function of X 1 and X 2 . That is, find an expression for P ( X 1 ≤ x 1 ,X 2 ≤ x 2 ) where x 1 ,x 2 ≥ . (b) Express the probability that Elena does not die as an expectation with respect to X 3 . That is, find g ( X 3 ) such that P ( Elena does not die ) = E X 3 [ g ( X 3 )] (c) Given that X 3 ∼ Gamma (10 , 2) , determine the probability that Elena does not die (provide a numerical value)....
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 Fall '08
 Chisholm
 Probability, Probability theory, Elena

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