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STAT 333 tutorial5

# STAT 333 tutorial5 - Stat 333 Tutorial 5 Fall 2011 1 In...

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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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STAT 333 tutorial5 - Stat 333 Tutorial 5 Fall 2011 1 In...

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