Question: 2. Consider a random sample X1, X2, ..., Xn from a distribution with probability function: f(x, ) = (1 ) x I{0,1,2,...}(x) a. Find the

2. Consider a random sample X1, X2, ..., Xn from a distribution with probability function: f(x, ) = (1 ) x I{0,1,2,...}(x)

a. Find the uniformly most powerful (UMP) test for testing the hypothesis Ho : o against H1 : > o. (2 points)

b. Find the likelihood ratio (LR) test for testing the hypothesis Ho : = o vs H1 : = o and compare (to see whether they are equivalent or not) with the union intersection test (UIT) constructed from the two one-sided UMP tests. (3 points)

c. By inverting the UIT or the LR test, find a 95% exact CI for and 1 . (2 points)

I wanted only part C fully

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