Q38Section I (Objective (Q1–Q80))38 of 80

Statistical Inference — moment estimator versus MLE

Consider the following for the next two (02) items: Let the probability density function $f_\theta(x) = \frac{1}{\theta}e^{-\frac{x}{\theta}}$ , $0 < x < \infty$ . Consider the following statements: I. The estimator of $\theta$ with methods of moment is equal to $2\overline{x}$ . II. Both maximum likelihood estimator and method of moments estimator will be same. Which of the statements given above is/are correct?

Pick an option to check your answer. In a mock test a wrong answer here costs 0.83 mark.

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