# $\LaTeX$ macros for expectation, variance and covariance?

Is it possible for Stack Exchange to make available $\LaTeX$ abbreviations for \mathrm{E}, \mathrm{Var}, \mathrm{Cov} (possibly with new commands \E, \Var and \Cov)? The problem is that things like $\mathrm{Var}[X\mid Y]$ look much better than $Var[X\mid Y]$, but we end up losing a lot of time typing that.

• Just FYI, you can also try: \$\text{Var}[X|Y]\$ (ie $\text{Var}[X|Y]$), if that's more convenient. Oct 5, 2012 at 18:08
• gung's suggestion saves two keystrokes, which is good, but I was wondering if \Var would make life easier for us. I understand that it would not be universally used, since it is not plain $\LaTeX$.
– Zen
Oct 5, 2012 at 18:13
• In my answers I often declare such a macro using \newcommand at the beginning and then use the macro in the rest of the answer. That's often helpful, especially if you need to use it many times. Oct 5, 2012 at 18:46
• (+1) Can I use \newcommand in my answers?!?!?!?!? Whoooaaaa! Problem solved. I'll setup a txt with definitions I normally use. Thank you a lot, Prof.!
– Zen
Oct 5, 2012 at 19:03
• @cardinal, I'm not familiar w/ \newcommand, since it seems that is the answer to this Q, can you make it official, perhaps w/ a brief tutorial re how it would work? Oct 5, 2012 at 20:18

$\newcommand{\E}{\mathrm{E}}$ $\newcommand{\Var}{\mathrm{Var}}$ $\newcommand{\Cov}{\mathrm{Cov}}$ $\newcommand{\Expect}{{\rm I\kern-.3em E}}$

$\newcommand{\E}{\mathrm{E}}$

$\newcommand{\Var}{\mathrm{Var}}$

$\newcommand{\Cov}{\mathrm{Cov}}$

After that, just use it. For example:

$$\Var[X] = \E[\Var[X\mid Y]] + \Var[[\E\mid X]]$$

$$\Cov[X,Y] = \E[XY] - \E[X]\E[Y]$$

$\newcommand{\Expect}{{\rm I\kern-.3em E}}$

$$\Expect[X]$$

which looks pretty.

• A somewhat fancier solution is $\newcommand{\Expect}{{\rm I\kern-.3em E}}$ that produces $\Expect[X]$. Unfortunately, you cannot easily extend it to the variance operator. Oct 6, 2012 at 2:28
• @Stas: That's an old hack for \mathbb E, i.e., $\mathbb E$. This does extend to variance $\mathbb V(X)$ or similar, as you like. The latter doesn't seem too popular though. :-) Oct 6, 2012 at 13:59
• Yay! Thanks, cardinal. I need to learn my $\LaTeX$ better, apparently :) Oct 6, 2012 at 15:08
• Neat solution. :) But I for one would prefer if these commands were available out-of-the-box. Oct 8, 2012 at 12:12
• (+1 a couple days ago) As a side note, if you want to avoid the empty space at the top of the answer caused by the macro definitions, you can just slip the \newcommand calls in at the beginning of the first math-mode block you use in your answer. :-) Oct 8, 2012 at 17:35
• (+1) Another great tip!
– Zen
Oct 8, 2012 at 20:15
• How do you use this? I have $\Var{\beta}$ but it misses those square brackets. How can you have them? Feb 28, 2015 at 21:21
• @Masi: \newcommand{\Var}{\operatorname{Var}\left[#1\right]} Sep 30, 2015 at 11:52
• Beware Although \newcommand is elegant and convenient, it appears to affect all $\TeX$ markup on the entire page--not just your individual post! This raises the prospect of bad interactions arising from conflicting commands in different posts (and even in comments). I suspect their processing might depend on the sequence in which the posts appear on the page. Thus, both arbitrary and future developments beyond your control could ruin your post!
– whuber Mod
Jul 8, 2016 at 18:48

To typeset an operator, it is much better to use \operatorname instead of \mathrm, as explained on tex.SE: What's the difference between \mathrm and \operatorname?

Compare (first line uses \mathrm, second line uses \operatorname): $$\mathrm{Var}[x] + 2\mathrm{Var}[y] - \mathrm{E}[x]\mathrm{E}[y]$$ $$\operatorname{Var}[x] + 2\operatorname{Var}[y] - \operatorname{E}[x]\operatorname{E}[y]$$ and notice small white spaces before the operator name in the second line.

As noted by @cardinal, MathJax supports \newcommand. The best way to use it is to put into the formula where the operator first appears, because putting it into a separate formula creates an annoying empty line (see @Zen's answer). So whenever you first need variance, you can type \newcommand{\Var}{\operatorname{Var}}, e.g.

$$\newcommand{\Var}{\operatorname{Var}} \Var[x]+\Var[y]$$


and this will be displayed as

$$\newcommand{\Var}{\operatorname{Var}} \Var[x]+\Var[y]$$

All subsequent formulas can simply use \Var in them, e.g. $\Var[z]$ will become $\Var[z]$.

For Corr, Cov and Var I usually use \DeclareMathOperator{\Corr}{Corr}, which, done once in an answer, allows me to just write \Corr(X,Y) whenever I need it later, which displays:

$$\DeclareMathOperator{\Corr}{Corr} \Corr(X,Y)$$

Like Amoeba's answer, this ensures spacing is done correctly in a way that \mathrm doesn't. But see newcommand vs. DeclareMathOperator on TEX.SE: Amoeba's answer apparently has the advantage that newcommand gives more flexibility.

But note I can still do \DeclareMathOperator{\E}{\mathbb{E}} \E(X,Y) and produce:

$$\DeclareMathOperator{\E}{\mathbb{E}} \E(X,Y)$$

And of course I can reuse these in a later piece of $\LaTeX$ too: $\E(X)+\Corr(X,Y)$

(In a document DeclareMathOperator can only be used in a preamble but this doesn't seem to cause any difficulty on here.)

• +1. This is perhaps a better way because it's slightly shorter: \DeclareMathOperator{\Corr}{Corr} vs. \newcommand{\Corr}{\operatorname{Corr}}. Sep 13, 2015 at 21:40
• This appealing answer; however, I've noticed that declaring operator through\DeclareMathOperator{\Cov}{Cov} printsCov using the document font (Arial in my case), it would be more presentable if the Cover would be printed with the same font as the text generated via \log and other similar commands. Feb 28, 2022 at 17:06