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Let X1 ,X2 , • • • ,X. be a random sample from a distribution with p.d.f. /( x; 8) = ex" - 1 , 0 x oo, zero elsewhere, where 8 > 0. Find a sufficient statistic for (J and show that a uniformly most powerful test of H0 : 8 == 6 against H1 : (J <>6 is based on this statistic.

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