# What is the formula for the standard error?

##### 1 Answer
May 12, 2018

$s e = \sqrt{\setminus m b \otimes \left\{v a r\right\} \left(X\right)}$

#### Explanation:

Given a random variable $X$ with a certain pdf $f$, the variance is

$\setminus m b \otimes \left\{v a r\right\} \left(X\right) = E \left({X}^{2}\right) - {E}^{2} \left(X\right) ,$ where $E$ is the expected value. The standard error (or standard deviation) is just $s e = \sqrt{\setminus m b \otimes \left\{v a r\right\} \left(X\right)} .$ For example, if $X$ is $N \left(\setminus \mu , \setminus {\sigma}^{2}\right)$, the standard error is $\setminus \sigma .$