please provide answers for all empty fields, failure to do so would result in bieng reported Let X be a random variable from a distribution with density /(x) = ox! for xe (0, 1) and otherwise, where 8 I is an unknown parameter. We want to verify the null hypothesis that 0 = 2 against the alternative that 8 = 6 for significance level 0.05 using a

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please provide answers for all empty fields, failure to do so would result in bieng reported

Let X be a random variable from a distribution with density /(x) = ox! for xe (0, 1) and otherwise, where 8 > I is an unknown parameter. We want to verify the null hypothesis that 0 = 2 against the alternative that 8 = 6 for significance level 0.05 using a test T with a critical region (X X > c), where e is the appropriate critical value • The value of e amounts to and the power of the test for the alternative hypothesis amounts to . Denote by MP the most powerful test for verifying the null hypothesis that 8 2 against the alternative that 6 for significance level 0.05. Then, MP Denote by PM the most powerful test for verifying the nut hypothesis that = 6 against the alternative that 0) = 2 for significance level 0.05. Then, PM Denote by MP2 the most powerful test for verifying the null hypothesis that 0 = 2 against the alternative that 0 = 6 for significance level 0-2. The test MP2 = Please provide numerical values rounded to two decimal digits

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