Let X1, , Xn be a random sample from the pdf f(x ) x 2, 0 x a What is a sufficient statistic for b Find the MLE of c Find the method of moment 's estimator of

Question: Let X1,..., Xn be a random sample from the pdf f(x|) = x-2, 0 < < x < . a. What is a sufficient

Let X1,..., Xn be a random sample from the pdf
f(x|θ) = θx-2, 0 < θ < x < ∞.
a. What is a sufficient statistic for θ?
b. Find the MLE of θ.
c. Find the method of moment's estimator of θ.

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