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Unformatted text preview: h 2 ( p 1 , p 2 ) 1 2 k p 1p 2 k 1 h ( p 1 , p 2 )[2h 2 ( p 1 , p 2 )] 1 / 2 . 4. Consider two probability measures P 1 and P 2 on a measurable space ( X , A ), dominated by a nite measure and let p 1 and p 2 be the densities of P 1 and P 2 with respect to , respectively. Show that the Hellinger distance h ( p 1 , p 2 ) does not depend on the dominating measure . 5. Given densities p and p , show h 2 ( p, p ) 16 h 2 ( p, p ) , where p = ( p + p ) / 2....
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 Fall '05
 MICHAELJORDAN
 Probability

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