\begin{block}{Expected value and variance of the mean}
If $X_1, \ldots, X_n$ are independent and identically distributed random variables with expected value $E[X_i] = \mu$ and variance $Var[X_i] = \sigma^2$, then the following holds for the mean of them, denoted $\bar X$:
\begin{align*}
E[\bar X] = \mu \\
Var[\bar X] = \frac{\sigma^2}{n}
\end{align*}
\end{block}