Question
Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ...
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Let Y1, Y2, . . . , Yn be independent and identically distributed Beta(θ, 1), θ > 0.
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(a) Find the MOM estimator for θ.
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(b) Find the ML estimator θˆ of θ.
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(c) Find the ML estimator τˆ of τ = P(Y1 ≤ a), for a ∈ (0,1).
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(d) Find a function of the ML estimator that is a pivotal quantity and use it to construct a two-sided
1−α CI for θ.
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Homework Answers
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