Let X1,X2, . . . , Xn be a random sample from the uniform distribution with...

Let X1,X2, . . . , Xn be a random sample from the uniform distribution with pdf f(x; θ₁, θ₂) = 1/(2θ₂), θ₁ − θ₂ < x < θ₁ + θ₂, where −∞ < θ₁ < ∞ and θ₂ > 0, and the pdf is equal to zero elsewhere.

(a) Show that Y1 = min(Xi) and Yn = max(Xi), the joint sufficient statistics for θ₁ and θ₂, are complete.

(b) Find the MVUEs of θ1 and θ2.

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orchestra answered 2 years ago

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