Dr. Hackney STA Solutions pg 124

Dr. Hackney STA Solutions pg 124 - Second Edition 8-3...

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Unformatted text preview: Second Edition 8-3 Differentiation will show that in the numerator = ( i x i + j y j ) / ( n + m ), while in the denominator = x and = y . Therefore, ( x , y ) = n + m i x i + j y j n + m exp- n + m i x i + j y j i x i + j y j n i x i n exp- n i x i i x i m j y j m exp- m j y j j y j = ( n + m ) n + m n n m m ( i x i ) n j y j m i x i + j y j n + m . And the LRT is to reject H if ( x , y ) c . b. = ( n + m ) n + m n n m m i x i i x i + j y j ! n j y j i x i + j y j ! m = ( n + m ) n + m n n m m T n (1- T ) m . Therefore is a function of T . is a unimodal function of T which is maximized when T = n m + n . Rejection for c is equivalent to rejection for T a or T b , where a and b are constants that satisfy a n (1- a ) m = b n (1- b ) m . c. When H is true, i X i gamma( n, ) and j Y j gamma( m, ) and they are indepen-...
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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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