Summary $\begin{aligned} E(\bar{X})&=\mu \end{aligned}$ $\begin{aligned} Var(\bar{X})&=\frac{\sigma^{2}}{n} \end{aligned}$ $\begin{aligned} sd(\bar{X})&=\frac{\sigma}{\sqrt{n}} \end{aligned}$ Let's prove the following summary 1. For a random sample size $n$ on $X$, where $E(X)=\mu$, we have $\begin{aligned} E(\bar{X})&=\mu \end{aligned}$ proof) Each random variable $X_{i}$ in the random sample h..