Let X1, , Xn be iid with pdf f(x ) x 1, 0 x 1, 0 a Find the MLE of , and show that its variance 0 as b Find the method of moments estimator of

Question: Let X1,..., Xn be iid with pdf f(x|) = x-1, 0 x 1, 0 < < a. Find the MLE of

Let X1,..., Xn be iid with pdf
f(x|θ) = θxθ-1, 0 ≤ x ≤ 1, 0 < θ < ∞
a. Find the MLE of θ, and show that its variance → 0 as → ∞.
b. Find the method of moments estimator of θ.

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