Suppose that a single observation X is taken from the uniform distribution on the interval [0, 0], where the value of e is unknown, and the following simple hypotheses are to be tested: Ho :0 = 1, H, :0 = 2. a. Show that there exists a test procedure for which a(ð) = 0 and B(d) < 1. b. Among all test procedures for which a(ð) = 0, find the one for which B(ð) is a minimum.

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Kindly provide answer for (a) and (b)

Suppose that a single observation X is taken from the uniform distribution on the interval [0, e],
where the value of e is unknown, and the following simple hypotheses are to be tested:
Ho : 0 = 1,
H,:0 = 2.
a. Show that there exists a test procedure for which a(õ) = 0 and B(0) < 1.
b. Among all test procedures for which a(õ) = 0, find the one for which B(O) is a minimum.
Transcribed Image Text:Suppose that a single observation X is taken from the uniform distribution on the interval [0, e], where the value of e is unknown, and the following simple hypotheses are to be tested: Ho : 0 = 1, H,:0 = 2. a. Show that there exists a test procedure for which a(õ) = 0 and B(0) < 1. b. Among all test procedures for which a(õ) = 0, find the one for which B(O) is a minimum.
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