Question: Let X 1 , . . . . , . X n be i.i.d. with pdf f ( x ; ) = 2 e x

Let X1,....,.Xn be i.i.d. with pdf

f(x;)=2exp(x)

i) Derive a likelihood ratio test of the hypothesis

H0:=0 vs. HA:=1

where 1>0 by specifying the simplest rejection region possible .

ii) Is the test UMP (uniformly most powerful) against the alternative HA:>0

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