Let X1, , Xn be a random sample from a population with pdf f(x ) x 1 , 0 x 1, 0 a Is Xi sufficient for b Find a complete sufficient statistic for

Question: Let X1,..., Xn be a random sample from a population with pdf f(x|) = x-1 , 0 < x < 1, > 0. a.

Let X1,..., Xn be a random sample from a population with pdf
f(x|θ) = θxθ-1 , 0 < x < 1, θ > 0.
a. Is ∑Xi sufficient for θ?
b. Find a complete sufficient statistic for θ.

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