Question: Suppose X is one observation from a population with Beta(0,1) PDF. For testing Ho : 0 1 vs H : 0 > 1, find

Suppose X is one observation from a population with Beta(0,1) PDF. For testing Ho : 0 1 vs H : 0 > 1, find the size and sketch the power function of the test that rejects Ho if X > 12. (b) Find the most powerful size-a test of Ho : 0 = 1 vs H0 = 2. (c) Consider a random sample X,..., Xn ~ iid Beta(0, 1). Using the entire sample, find the UMP size-a test. You should be able to write the rejection region in terms of a critical value from a x2 distribution. (d) Find the power (as a function of the sample size n) at 0 = 2.

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