You should have noticed by now that repeatedly sampling from a given distribution has yields a variety of sample statistics such as the sample mean, the sample variance and relative frequency. In each instance, these descriptive statistics obtained by performing a particular experiment over and over seemed to "stabilize" around some limiting value. It might be sensible to presume that
\begin{equation*}
\overline{x} \approx \mu
\end{equation*}
would be a good estimate for the population mean or
\begin{equation*}
\frac{Y}{n} \approx p
\end{equation*}
would be a good estimate for the population likelihood of success or
\begin{equation*}
s^2 \approx \sigma^2
\end{equation*}
would be a good estimate for the population variance. A rigorous investigation that is beyond the scope of this text would validate that these sample statistics are indeed good estimators when you don’t know the theoretical measures. This will be addressed more directly in
the section on Point Estimates 10.3.