Question-22

MLE

Let \(X_1, \ldots, X_n\sim \text{i.i.d. Uniform}(-a, a).\) Find the ML estimator of \(a.\)

\(\hat{a}_{ML}= \dfrac{1}{2^n}\max(X_1, \dots, X_n)\)
\(\hat{a}_{ML}=\max(X_1, \dots, X_n)\)
\(\hat{a}_{ML}=\min(X_1, \dots, X_n)\)
\(\hat{a}_{ML}= \dfrac{1}{2^n}\min(X_1, \dots, X_n)\)

Hint

Apply the method of MLE

Answer

\(\hat{a}_{ML}= \dfrac{1}{2^n}\max(X_1, \dots, X_n)\)
\(\hat{a}_{ML}=\max(X_1, \dots, X_n)\)
\(\hat{a}_{ML}=\min(X_1, \dots, X_n)\)
\(\hat{a}_{ML}= \dfrac{1}{2^n}\min(X_1, \dots, X_n)\)

Solution