Question: 10. Let Xl' . .. ' Xn be independently distributed with density (2fJ)-le- x / 2I1 , x 0, and let YI ;5;

10. Let Xl' . .. ' Xn be independently distributed with density (2fJ)-le- x / 2I1 , x 0, and let YI ;5; •• • ;5; y" be the ordered X's. Assume that YI becomes available first, then Y2 , and so on, and that observation is continued until Y,. has been observed. On the basis of YI , ... , Y,. it is desired to test H : fJ fJo = 1000 at level a = .05 against fJ < fJo. (i) Determine the rejection region when r = 4, and find the power of the test against fJI = 500. (ii) Find the value of r required to get power p .95 against this alternative. [In Problem 14, Chapter 2, the distribution of [L~_IYi + (n - r)y"JlfJ was found to be X2 with 2r degrees of freedom.]

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