# ONLY A) B) D) 4 Let X be a single observation from the density f(x; 0)=...

###### Question:

ONLY A) B) D)

4 Let X be a single observation from the density f(x; 0)= Ox® -110, 1)(x), where 0 >0. (a) In testing Ho: 0 <1 versus H 1:8 > 1, find the power function and size of the test given by the following: Reject H , if and only if X > . (6) Find a most powerful size-a test of Ho:8=2 versus H 1:0= 1. (c) For the loss function given by [(do; 2) = f(d1; 1)=0, ((do; 1)=((dı; 2)=1, find the minimax test of H.:0=2 versus H 1:0= 1. (d) Is there a uniformly most powerful size-a test of Ho:8 > 2 versus H 1:8< 2? If so, what is it? (e) Among all possible simple likelihood-ratio tests of H.: 0= 2 versus H 1: 0= 1, find that test that minimizes a + B, where a and B are the respective sizes of the Type I and Type II errors. () Find the generalized likelihood-ratio test of size a of Ho: Q=1 versus H 1:0 +1.

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