Variance of sample mean squared

It is well known that $\bar X^2$ is a biased estimator for $\mu^2$, but a little is known to its variance. Before we start working on $Var(\bar X^2)$, let’s recall that $\bar X$ is an unbiased estimator for $\mu$, i.

Why unbaised estimator?

In introductory statistics courses, we often focus on unbiased estimators such as the sample variance, $$ S^2 = \frac{\sum(X_i - \bar X)^2}{n - 1} $$ rather than a more initiative estimator $$ \hat \sigma^2 = \frac{\sum(X_i - \bar X)^2}{n}.

Girl ratio The Zorganian Republic has some very strange customs. Couples only wish to have female children as only females can inherit the family’s wealth, so if they have a male child they keep having more children until they have a girl.