4. (15 marks) Let (x1, x2, ..., xn) be i.i.d. samples of a random variable X with mean ? and variance ?², where n > 3. Consider the following estimators of ?: ??? = 1/n ?_{i=1}^{n} x? ??? = (2x? - x? + x?) / 2 (a) Is either estimator unbiased? (b) Which of these two estimators is better? In what sense is it better?
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Given the estimators: \[ \hat{\mu}_{1} = \frac{1}{n} \sum_{i=1}^{n} x_{i} \] \[ \hat{\mu}_{2} = \frac{2x_{1} - x_{2} + x_{3}}{2} \] Show more…
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