Let X1, X2, . . . , Xn be iid following a uniform distribution over the...

Let X1, X2, . . . , Xn be iid following a uniform distribution over the interval (θ, 2θ) (θ > 0).

(a) Find a method of moments estimator of θ.

(b) Find the MLE of θ.

(c) Find a constant k such that E(k ˆθ) = θ.

(d) By using the Rao-Blackwell, which estimators of (a) and (b) can be improved?

Expert Solution

Solution :- X vid , Xg-..YAN U(.20), (670). (a) UN UCB) ab) : Mme is equate =Elx)= first moment with E(X) 6) GSXw sye ..... Xess ? 20. e CXC. XCO <26. =beden, Xcas co. Likelinoo function MIEtet: Mart Lio) = *c) 4 6 4 ) Likelihood function Lio) will be maximum cu hoa bois minimumi MLECO) = Xeno

orchestra answered 2 years ago

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