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# 3. Let X,Xn iid Unif(o,0) . Is this family MLR in Y = Xo)?(b) Find the UMP size-a test for Ho : 0 < 0 vs H, : 0 > 0 Find the UMP size-a test for Ho : 0 2 0o v...

## Question

###### 3. Let X,Xn iid Unif(o,0) . Is this family MLR in Y = Xo)?(b) Find the UMP size-a test for Ho : 0 < 0 vs H, : 0 > 0 Find the UMP size-a test for Ho : 0 2 0o vs Hs : 0 < 0 Letting R be the rejection region for the test in part (b) and Rz be the rejection region for the test in part (c) Consider the test for the hypotheses Ho 0 = 0 vs H : 0 # O determined by the rejection region R= Ri U Rz. That is, we reject Ho if the data is in either Ru Find the power function of this test and comment

3. Let X, Xn iid Unif(o,0) . Is this family MLR in Y = Xo)? (b) Find the UMP size-a test for Ho : 0 < 0 vs H, : 0 > 0 Find the UMP size-a test for Ho : 0 2 0o vs Hs : 0 < 0 Letting R be the rejection region for the test in part (b) and Rz be the rejection region for the test in part (c) Consider the test for the hypotheses Ho 0 = 0 vs H : 0 # O determined by the rejection region R= Ri U Rz. That is, we reject Ho if the data is in either Ru Find the power function of this test and comment on the size. or Rz_

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