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In: Statistics and Probability

Let X1, X2, · · · , Xn be iid samples from density: f(x) = {θx^(θ−1),...

Let X1, X2, · · · , Xn be iid samples from density:

f(x) = {θx^(θ−1), if 0 ≤ x ≤ 1}

0 otherwise

Find the maximum likelihood estimate for θ. Explain, using Strong Law of Large Numbers, that this maximum likelihood estimate is consistent.

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