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Unformatted text preview: > z  x ) P ( X = x ) = X x =1 x Y i =1 P ( U i > z ) P ( X = x ) (by independence of the U i s) = X x =1 P ( U i > z ) x P ( X = x ) = X x =1 (1z ) x 1 ( e1) x ! = 1 ( e1) X x =1 (1z ) x x ! = e 1z1 e1 < z < 1 . 5.24 Use f X ( x ) = 1 / , F X ( x ) = x/ , 0 < x < . Let Y = X ( n ) , Z = X (1) . Then, from Theorem 5.4.6, f Z,Y ( z,y ) = n ! 0!( n2)!0! 1 1 z yz n2 1y = n ( n1) n ( yz ) n2 , < z < y < ....
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 Spring '12
 Dr.Hackney
 Statistics

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