Question: Let X1, . . . ,Xn be i.i.d r.v. with the p.d.f. mm = g expt lrl m a: e R, where 8 > 0

Let X1, . . . ,Xn be i.i.d r.v. with the p.d.f. mm = g expt lrl m a: e R, where 8 > 0 is unknown parameter. Consider the hypotheses Ha : 9 : 1 against H1 : 9 > 1. (a) Check whether this p.d.f. is in the Exponential class and whether the likelihood ratio satises the monotonicity condition. (b) ' Construct the UMP test for testing H0 against H1 at significance level or = 0.05. (It is OK to use a variable instead of a quantile, but one needs to explain what quantile is used in the solution.) (c) Find an expression for the power function for the constructed test

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