Question: Problem 2. Let X1, ..., Xn be independent random variables with common density po(x) = (rx-10) exp(-x0)1[x > 0] for some unknown 0 > 0

Problem 2. Let X1, ..., Xn be independent random variables with common density po(x) = (rx"-10) exp(-x0)1[x > 0] for some unknown 0 > 0 and some known r > 0. (1) Show that T = 1 X7 is a complete sufficient statistic. (2) Find a density of XTO. (3) Show that {It : t > 0} is a pivotal quantity and determine the pivotal distribution. (4) Construct a 1 - o confidence interval for 0. (5) Find the MLE of 9

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