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(Solved): 1. Let \( \left\{X_{1}, \ldots \ldots X_{10}\right\} \) be a random sample of 10 observations obtai ...




1. Let \( \left\{X_{1}, \ldots \ldots X_{10}\right\} \) be a random sample of 10 observations obtained from a population havi
1. Let \( \left\{X_{1}, \ldots \ldots X_{10}\right\} \) be a random sample of 10 observations obtained from a population having a mean \( \mu \) and variance \( \sigma^{2} \). Consider the following estimators of \( \mu \) : \[ \begin{array}{r} \hat{\mu}_{1}=\frac{1}{10} \sum_{i=1}^{10} X_{i} \\ \hat{\mu}_{2}=\frac{1}{9} \sum_{i=1}^{10} X_{i} \end{array} \] (a) Are the two estimators unbiased? (b) Is it true that \( \operatorname{Var}\left(\hat{\mu}_{2}\right)>\operatorname{Var}\left(\hat{\mu}_{1}\right) \) ?


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1. (a) we are given with the two estimators ?^1and?^2.
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