Question: 4) Let X1, X2, ...Xn are i.i.d random sample from a Weibull distribution with pdf (30 points) Ba 3-1 f (2; a) exp a )I(x

4) Let X1, X2, ...Xn are i.i.d random sample from a Weibull distribution with pdf (30 points) Ba 3-1 f (2; a) exp a )I(x > 0) where a > 0 is unknown but 3 > 0 is known. a) Show that the distribution of Y = X, is Exp(@), for i = 1, 2, ..n. (Use Jacobian Transformation). b) Show that the RR of the MP (Most Powerful) test for testing Ho : 0 = 00 VS H1 : 0 = 01 (>00), is X > c (c is any known number) c) Show that for fixed size o, (level of significance of the test), find the exact expression of c= y

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