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8.70 - The PDF of an exponential distribution is III a =...

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Unformatted text preview: The PDF of an exponential distribution is III ; a] = int? I :3 m We start by finding the Likelihood function u —5.;2I, _ it, E Ethxn =TU'III-Hu = Ede ' = flea—"E I If Hie probabiLity densityfunction isfglx], flienTis sufficient for S if and only iffunctions g- and 1": can be found such ‘H’1El‘l: fall?) 2 him) 93 (11(3)): ireplacefi' wifli A] i.e. fJ'ie densityf can be factored into a product suchfl'iat one factor, 1'}, does not depend on 9 andfl'ie ofl'ier factor, which does depend on El, depends onx only Through Tlx]. In This example, Tlx] = :1 .‘According to die factorization flieorern, Ex,- I Tlx] = n is a sufficient statistic for in. 2x]: I ...
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