Let X₁....., X_n(n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X̅ = \(\rm \frac{1}{n}\Sigma_{n=1}^nX_i, X_{(1)}=min\{X_1....X_n\}\) and X_(n) = max {X₁....., X_n}. Which of the following statements are true?

Maximum likelihood estimator of θ is min \(\rm \left\{X_{(1)}, \frac{X_{(n)}}2{}\right\}\)

Maximum likelihood estimator of θ is max \(\rm \left\{-X_{(1)}, \frac{X_{(n)}}2{}\right\}\)

Method of moments estimator of θ is 2X̅

Method of moments estimator of θ is \(\rm \frac{2\bar X}{3}\)

Let X1....., Xn(n ≥ 2) be a random sample from a U(-θ, 2θ) distribution, where θ > 0 is an unknown parameter. Let X̅ = \(\rm \frac{1}{n}\Sigma_{n=1}^nX_i, X_{(1)}=min\{X_1....X_n\}\) and X(n) = max {X1....., Xn}. Which of the following statements are true?