Question: 1. Consider i.i.d. uniform random variables X1, ..., Xn on [0, 0]. Let Yn = max{X1, ..., Xn}. Given Yn, we would like to test

1. Consider i.i.d. uniform random variables X1, ..., Xn on [0,

1. Consider i.i.d. uniform random variables X1, ..., Xn on [0, 0]. Let Yn = max{X1, ..., Xn}. Given Yn, we would like to test Ho : 0 = 00 against H1 : 0 > 00. (The Wald test does not apply here because Yn is not asymptotically Gaussian.) (a) What is the CDF of Yn? (b) Based on the distribution of Yn, what is an appropriate test at significance level a E (0, 1)? (c) What is the power function of this test? What is the limit of the power at 0 > do as n -> oo

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