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I need a solution to this question. Thank you in advance. 3. (20 points) Let X1, ..., X, be a sample from a population with

I need a solution to this question. Thank you in advance.

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3. (20 points) Let X1, ..., X, be a sample from a population with density p(x, 0) given by p(x, 0) = _ exp { _(7 - 8) ] if r > / and 9 p(I, 0) = 0 otherwise . Here 0 = (#, 5) with -0o 0. (a) Show that min {X1, ..., X, } is sufficient for a when o is fixed. (b) Find a one-dimensional sufficient statistic for o when u is fixed. (c) Exhibit a two-dimensional sufficient statistic for 0

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