Question: Let X1, X2, and X3 be a random sample of size three from a uniform(, 2) distribution, where > 0. (a) Find the method

Let X1, X2, and X3 be a random sample of size three from a uniform(θ, 2θ) distribution, where θ > 0.
(a) Find the method of moments estimator of θ.
(b) Find the MLE, θ, and find a constant k such that Eθ(kθ) = θ.
(c) Which of the two estimators can be improved by using sufficiency? How?
(d) Find the method of moments estimate and the MLE of θ based on the data
1.29, .86, 1.33,
three observations of average berry sizes (in centimeters) of wine grapes.

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