Exercise 6. Let 0> 0 and XU[0,0], i.e. X is uniformly distributed on the interval [0,0]. a) As a function of 0, determine P(X ≤ 1). b) Assume that 0 is unknown, but we can observe X. For given Oo, we want to test the hypothesis H: 020 against the alternative H₁: 0 < 0o. Consider the test which rejects Ho, if and only if X < c. dow should we choose c, as a function of 0o and a, to get a test with significance level a? Carefully justify your answer.

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