3.19 a. $\bar{Y}$ is an unbiased estimator of $\mu_Y$. Is $\bar{Y}^2$ an unbiased estimator of $\mu_{\bar{Y}}^2$? b. $\bar{Y}$ is a consistent estimator of $\mu_Y$. Is $\bar{Y}^2$ a consistent estimator of $\mu_{\bar{Y}}^2$?
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An estimator $T$ is unbiased for a parameter $\theta$ if $E[T] = \theta$. We are given that $\bar{Y}$ is an unbiased estimator of $\mu_Y$, which means $E[\bar{Y}] = \mu_Y$. We need to check if $E[\bar{Y}^2] = \mu_{\bar{Y}}^2$. Recall the formula for variance: Show more…
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