Question: Suppose that a single observation X is to be drawn from an unknown distribution P, and that the following simple hypotheses are to be tested:

Suppose that a single observation X is to be drawn from an unknown distribution P, and that the following simple hypotheses are to be tested:
H0: P is the uniform distribution on the interval [0, 1],
H1: P is the standard normal distribution.
Determine the most powerful test of size 0.01, and calculate the power of the test when H1 is true.

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