Question: 6. [20 points] Let X1,..., Xn be a random sample from the distribution for parameter 0 > 0. 0 f(x | 0) = x

6. [20 points] Let X1,..., Xn be a random sample from the distribution for parameter 0 > 0. 0 f(x | 0) = x > 0, (1+x)1+0' (a) Find the MLE for 0. (b) Find the Fisher information Z(0) of a single observation. (c) Propose a Wald test for the hypotheses Ho: 000 vs H:0>00- (d) Between the Karlin-Rubin test in problem 5c and the Wald test in 6c, which test do you prefer? Justify your choice in a sentence or two.

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