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Let X1, ..., X. be i.i.d. random variables with pdf f (x) = 01-, r E (0, 1), # E (0, 00). 1. What is

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Let X1, ..., X. be i.i.d. random variables with pdf f (x) = 01-, r E (0, 1), # E (0, 00). 1. What is the likelihood function? (4 points) 2. Find a one-dimensional sufficient statistic for 8. Note that the vector (X1, ..., X ) is sufficient by definition, but it is n-dimensional. (7 points) 3. Find the method of moment estimator for 0. (7 points) 4. It is consistent? Prove your result. (7 points)

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