Consider a random sample of size one (n = 1) from the distribution with probability function -{0(0-1), if << 1 for >0 otherwise. f(y;0)= (a) To test Ho: 0 = 0, versus H₁ : 0 = 0₁ > 0o, find a most powerful test. Let the positive constant to define the rejection region of the test be k. (d) Graph the power function against for k=0.3, 0.5, 0.8, and comment on how the power of the test changes as the values of k and change. (e) Is the above test in part (a) a uniformly most powerful test? Justify your answer.

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