22. If fJ ((J) denotes the power function of the UMP test of Corollary 2, and if...

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22. If fJ ((J) denotes the power function of the UMP test of Corollary 2, and if the function Q of (12) is differentiable, then fJ'((J) > 0 for all (J for which Q'«(J) > O. [To show that {J'«(Jo) > 0, consider the problem of maximizing, subject to Eoo (X) =

a, the derivative fJ'((Jo) or equivalently the quantity Eoo[T(X)(X)].]

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