Dr. Hackney STA Solutions pg 89

Dr. Hackney STA Solutions pg 89 - Second Edition 6-3 e. Fix...

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Unformatted text preview: Second Edition 6-3 e. Fix sample points x and y . Define A ( ) = { i : x i } , B ( ) = { i : y i } , a ( ) = the number of elements in A ( ) and b ( ) = the number of elements in B ( ). Then the function f ( x | ) /f ( y | ) depends on only through the function n X i =1 | x i- | - n X i =1 | y i- | = X i A ( ) ( - x i ) + X i A ( ) c ( x i- )- X i B ( ) ( - y i )- X i B ( ) c ( y i- ) = ( a ( )- [ n- a ( )]- b ( ) + [ n- b ( )]) + - X i A ( ) x i + X i A ( ) c x i + X i B ( ) y i- X i B ( ) c y i = 2( a ( )- b ( )) + - X i A ( ) x i + X i A ( ) c x i + X i B ( ) y i- X i B ( ) c y i . Consider an interval of s that does not contain any x i s or y i s. The second term is constant on such an interval. The first term will be constant, on the interval if and only if a ( ) = b ( )....
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This note was uploaded on 02/03/2012 for the course STA 1014 taught by Professor Dr.hackney during the Spring '12 term at UNF.

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